If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.

If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.
by

1 Answer

Answer :

If one roots of the equation `x^(2) - mx + n = 0` is twice the other root, then show that `2m^(2) = 9pi`.
by

Related questions

If `alpha, beta` are the roots of the quadratic equation `lx^(2) + mx + n = 0`,then evaluate the following expressions. (a) `alpha^(2) + beta^(2)` (b)

Description : If `alpha, beta` are the roots of the quadratic equation `lx^(2) + mx + n = 0`,then evaluate the following expressions. (a) `alpha^(2) + beta^(2)` (b)

Last Answer : If `alpha, beta` are the roots of the quadratic equation `lx^(2) + mx + n = 0`,then evaluate the following ... ) `1/(alpha^(3)) + 1/(beta^(3))`

If x^2 + mx + n = 0 and x^2 + px + q = 0 have a common root, then the common root is -Maths 9th

Description : If x^2 + mx + n = 0 and x^2 + px + q = 0 have a common root, then the common root is -Maths 9th

Last Answer : Let α be the common root ∴α2+pα+q=0 ...........(1) and α2+qα+p=0 ........ (2) Solving (1) & (2), we get, p2−q2α2​=q−pα​=q−p1​∴α=q−pp2−q2​ and α=1 ⇒q−pp2−q2​=1 ⇒p2−q2=q−p (or) (p2−q2)+(p−q)=0 ⇒(p−q)[p+q+1]=0 ⇒p−q=0 or p+q+1=0

For what value of m the ratio of the roots of the equation 12x^2 – mx + 5 = 0 is 3 : 2 ? -Maths 9th

Description : For what value of m the ratio of the roots of the equation 12x^2 – mx + 5 = 0 is 3 : 2 ? -Maths 9th

Last Answer : Given equation: 12x2+mx+5=0 The roots are in ratio 3:2 Hence,let roots of the equations are 3α and 2α. Applying condition for sum and product of the roots, 3α+2α=−12m​ and 3α×2α=125​⇒α2=725​⇒α=±62​5​​And m=−60α ⇒m=±510​Hence, A is the correct option.

For what values of m does the equation, `mx^(2) + (3x-1)m + 2x + 5 = 0` have equal roots of opposite sign ?

Description : For what values of m does the equation, `mx^(2) + (3x-1)m + 2x + 5 = 0` have equal roots of opposite sign ?

Last Answer : For what values of m does the equation, `mx^(2) + (3x-1)m + 2x + 5 = 0` have equal roots of opposite sign ?

If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of circle `S_2=0` which touches `S_1=0` at `(0,0)`

Description : If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of circle `S_2=0` which touches `S_1=0` at `(0,0)`

Last Answer : If `16l^2+9m^2=24lm+6l+8m+1` and the line `mx+ly=1` is tangent to circle `S_1=0` then the equation of ... `3x^(2)+3y^(2)-8x-6y=0` D. none of theese

if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root

Description : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive root

Last Answer : if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the ... `1` D. third term is `(-1+sqrt(11))/(2)`

The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 is -Maths 9th

Description : The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 is -Maths 9th

Last Answer : answer:

If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Description : If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Last Answer : answer:

If `alpha, beta` are roots of equation `x^(2)-4x-3=0` and `s_(n)=alpha^(n)+beta^(n), n in N` then the value of `(s_(7)-4s_(6))/s_(5)` is

Description : If `alpha, beta` are roots of equation `x^(2)-4x-3=0` and `s_(n)=alpha^(n)+beta^(n), n in N` then the value of `(s_(7)-4s_(6))/s_(5)` is

Last Answer : If `alpha, beta` are roots of equation `x^(2)-4x-3=0` and `s_(n)=alpha^(n)+beta^(n), n in N` then the value ... 4s_(6))/s_(5)` is A. 4 B. 3 C. 5 D. 7

A satellite of mass "M" is in orbit around the earth. If a second satellite of mass "2M" is to be placed in the same orbit, the second satellite must have a velocity which is: w) half the velocity of the first satellite x) the same as the velocity of the first satellite y) twice the velocity of the first satellite z) four times the velocity of the first satellite

Description : A satellite of mass "M" is in orbit around the earth. If a second satellite of mass "2M" is to be placed in the same orbit, the second satellite must have a velocity which is: w) half ... first satellite y) twice the velocity of the first satellite z) four times the velocity of the first satellite

Last Answer : ANSWER: X -- THE SAME AS THE VELOCITY OF THE FIRST SATELLITE 

If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Description : If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Last Answer : Let l+m−2nlogx​=m+n−2llogy​=n+l−2mlogz​=k(say) So, we get logx=k(l+m−2n) ....... (i) logy=k(m+n−2l) ....... (ii) logz=k(n+l−2m) ....... (iii) ∴logx+logy+logz=k(l+m−2n)+k(m+n−2l)+k(n+l−2m) ⇒logx+logy+logz=kl+km−2kn+km+kn−2kl+kn+kl−2km ⇒log(xyz)=0 ⇒logxyz=log1 ⇒xyz=1

If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Description : If (log x)/(l + m - 2n) = (log y)/(m + n - 2l) = (log z)/(n + l - 2m), then xyz is equal to : -Maths 9th

Last Answer : (b) 1Let \(rac{ ext{log}\,x}{l+m-2n}\) = \(rac{ ext{log}\,y}{m+n-2l}\) = \(rac{ ext{log}\,z}{n+l-2m}\) = k. Thenlog x = k(l + m – 2n), log y = k(m + n – 2l); log z = k(n + l – 2m) ⇒ log x + log y + log z = k(l + m – 2n) + k(m + n – 2l) + k(n + l – 2m)⇒ log(xyz) = 0 ⇒ log(xyz) = log 1 ⇒ xyz = 1.

If the difference in the roots of the equation x^2 – px + q = 0 is unity, then which one of the following is correct ? -Maths 9th

Description : If the difference in the roots of the equation x^2 – px + q = 0 is unity, then which one of the following is correct ? -Maths 9th

Last Answer : answer:

If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

Description : If the roots of the equation x^2 – 2ax + a^2 + a – 3 = 0 are real and less than 3, then which one of the following is correct ? -Maths 9th

Last Answer : answer:

If the roots of the equation a(b – c) x^2 + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in : -Maths 9th

Description : If the roots of the equation a(b – c) x^2 + b(c – a)x + c(a – b) = 0 are equal, then a, b, c are in : -Maths 9th

Last Answer : As we know that for the quadratic equation ax2+bx+c=0, roots will be equal if D=B2−4AC=0 Therefore, for the equation, a(b−c)x2+b(c−a)x+c(a−b)=0 A=a(b−c),B=b(c−a),C=c(a−b) D=0 B2−4AC=0 (b(c−a))2−4(a(b−c))(c(a−b))=0 ⇒ab+bc=2ac Hence a,b and c are in HP.

If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

Description : If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

Last Answer : Let the roots of the equation x3 – ax2 + bx – c = 0 be (α – 1), α, (α + 1) ∴ S2 = (α – 1)α + α(α + 1) + (α + 1) ( ... ; 1 = b ⇒ 3α2 – 1 = b ∴ Minimum value of b = – 1, when α = 0.

If the equation (a^2 + b^2) x^2 – 2 (ac + bd)x + (c^2 + d^2) = 0 has equal roots, then which one of the following is correct ? -Maths 9th

Description : If the equation (a^2 + b^2) x^2 – 2 (ac + bd)x + (c^2 + d^2) = 0 has equal roots, then which one of the following is correct ? -Maths 9th

Last Answer : The given quadratic equation is (a2 + b2)x2 − 2(ac + bd)x + (c2 + d2) = 0. If the roots of given quadratic equation are equal, then its discriminant is zero.

If the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c. -Maths 10th

Description : If the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c. -Maths 10th

Last Answer : following is the equation of 2b = a+c =

If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc -Maths 10th

Description : If the roots ff the equation (c2 – ab)x2 – 2(a2 – bc)x + b2 – ac = 0 are equal, then prove that either a = 0 or a3 + b3 + c3 = 3abc -Maths 10th

Last Answer : (c2 – ab) x2 + 2(bc - a2 ) x+ (b2 – ac) = 0 Comparing with Ax2 + Bx + C = 0 A = (c2 – ab), B = 2(bc - a2 ) and C = b2 – ac According to the question, B2 - 4AC = 0 Put the values in the above equation we get 4a(a3 + b3 + c3 -3abc) = 0 hence, a = 0 or a3 + b3 + c3 = 3ab

If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of

Description : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then the maximum value of the sum of the squares of

Last Answer : If `alpha, beta` are the roots of the equation `x^2 + (sin phi -1)x-1/2 cos^2 phi = 0 (phi in R),` then ... the roots is. A. 4 B. 3 C. `9//4` D. 2

If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

Description : If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

Last Answer : If `alpha` and `beta` are the roots of the quadratic equation `x^(2) + 3x - 4 = 0`, then `alpha^(-1) + beta^(-1) = "_____"`.

If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

Description : If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

Last Answer : If `k_(1)` and `k_(2)` are roots of `x^(2) - 5x - 24 = 0`, then find the quadratic equation whose roots are `-k_(1)` and `-k_(2)`.

If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

Description : If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

Last Answer : If `2alpha` and `3beta` are the roots of the equation `x^(2) + az +b = 0`, then find the equation whose roots are `a,b`.

If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.

Description : If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.

Last Answer : If a, b are the roots of the equation `x^(2) - px +q = 0`, then find the equation which has `a/b` and `b/a` as its roots.

If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

Description : If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

Last Answer : If `-3` and 4 are the roots of the equation `(x+k) (x-4) =0` , then the value of k is `"______"`.

If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315]` is equal to `kpi`, then the value of

Description : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315]` is equal to `kpi`, then the value of

Last Answer : If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315 ... is A. `10` B. `20` C. `50` D. `80`

The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + s/m X x = 0 If the roots of this equation are real, then the system will be A. over damped B. under damped C. critically damped D. none of the mentioned

Description : The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + s/m X x = 0 If the roots of this equation are real, then the system will be A. over damped B. under damped C. critically damped D. none of the mentioned

Last Answer : A. over damped

The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + k/m X x = 0 If the roots of this equation are real, then the system will be a) over damped b) under damped c) critically damped d) none of the mentioned Ans:a

Description : The equation of motion for a vibrating system with viscous damping is d 2 x/dt 2 + c/m X dx/dt + k/m X x = 0 If the roots of this equation are real, then the system will be a) over damped b) under damped c) critically damped d) none of the mentioned Ans:a

Last Answer : a) over damped

If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, the numerically greater root has `"_____"` sign. [p

Description : If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, the numerically greater root has `"_____"` sign. [p

Last Answer : If the sum of the roots of a quadratic equation, is positive and product of the roots is negative, ... root has `"_____"` sign. [positive/negative]

For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Description : For what value of m will the expression 3x^3 + mx^2 + 4x – 4m be divisible by x + 2 ? -Maths 9th

Last Answer : f(x) = 3x3 + mx2 + 4x – 4m f(x) is divisible by (x + 2) if f(–2) = 0 Now f(–2) = 3(–2)3 + m(–2)2 + 4(–2) – 4m = – 24 + 4m – ... ; 4m = – 32 ≠ 0 ∴ No such value of m exists for which (x + 2) is a factor of the given expression

What is y=mx+b for (-3,-3) and (0,-4)?

Description : What is y=mx+b for (-3,-3) and (0,-4)?

Last Answer : y = -1/3x - 4

A cantilever of length 3m carries a uniformly distributed load of 15KN/m over a length of 2m from the free end.If I= 108 mm4 and E= 2×105 N/mm2,find the slope at the free end? a.0.00326 rad b.0.00578 rad c.0.00677 rad d.0.00786 rad

Description : A cantilever of length 3m carries a uniformly distributed load of 15KN/m over a length of 2m from the free end.If I= 108 mm4 and E= 2×105 N/mm2,find the slope at the free end? a.0.00326 rad b.0.00578 rad c.0.00677 rad d.0.00786 rad

Last Answer : a.0.00326 rad

A cantilever of length 2m carries a point load of 30KN at the free end.If I = 108 mm4 and E= 2×105 N/mm2. What is the slope of the cantilever at the free end? a.0.503 rad b.0.677 rad c. 0.003 rad d.0.008

Description : A cantilever of length 2m carries a point load of 30KN at the free end.If I = 108 mm4 and E= 2×105 N/mm2. What is the slope of the cantilever at the free end? a.0.503 rad b.0.677 rad c. 0.003 rad d.0.008

Last Answer : c. 0.003 rad

If one root of the equation ax^2 + x – 3 = 0 is –1, then what is the other root ? -Maths 9th

Description : If one root of the equation ax^2 + x – 3 = 0 is –1, then what is the other root ? -Maths 9th

Last Answer : answer:

n which of the following cases, overdamping occurs? a) Roots are real b) Roots are complex conjugate c) Roots are equal d) Independent of the equation

Description : n which of the following cases, overdamping occurs? a) Roots are real b) Roots are complex conjugate c) Roots are equal d) Independent of the equation

Last Answer : a) Roots are real

If the roots of the equation ax^2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ? -Maths 9th

Description : If the roots of the equation ax^2 + bx + c = 0 are equal in magnitude but opposite in sign, then which one of the following is correct ? -Maths 9th

Last Answer : answer:

If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Description : If the sum of the roots of the equation ax^2 + bx + c = 0 is equal to the sum of their squares, then which one of the following is correct ? -Maths 9th

Last Answer : Given equation: ax2+bx+c=0 Let α and β be the roots of given quadratic equation Sum of the roots i.e. α+β=a−b Product of roots i.e. αβ=ac It is given that, Sum of the roots = Sum of squares of the roots i ... )2−2αβ i.e. a−b =(a−b )2−a2c i.e. −ab=b2−2ac i.e. ab+b2=2ac Hence, C is the correct option.

The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0

Description : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , then `lambda` can be equal to 0

Last Answer : The equation `2sin^3theta+(2lambda-3)sin^2theta-(3lambda+2)sintheta-2lambda=0` has exactly three roots in `(0,2pi)` , ... -1 B. 0 C. `(1)/(2)` D. 1

If the roots of the quadratic equation `4x^(2) -16x + p = 0`, are real and unequal, then find the value/s of p.

Description : If the roots of the quadratic equation `4x^(2) -16x + p = 0`, are real and unequal, then find the value/s of p.

Last Answer : If the roots of the quadratic equation `4x^(2) -16x + p = 0`, are real and unequal, then find the value/s of p.

If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

Description : If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

Last Answer : If the discriminant of the equation `ax^(2) + bx + c = 0` is greater than zero, then the roots are `"______"`.

If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

Description : If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

Last Answer : If the equation `3x^(2) - 2x-3 = 0`has roots `alpha`, and `beta` then `alpha.beta = "______"`.

The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

Description : The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

Last Answer : The roots of a quadratic equation `ax^(2) + bx + c=0` are 1 and `c/a`, then `a + b = "_____"`.

If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?

Description : If the equation x2 minus ax plus 2b equals 0 has prime roots where a and b are positive integers then a minus b is equal to?

Last Answer : I think you mean the roots are prime numbers.Let the two roots be primes p and qThen the equation factorises to (x - p)(x - q) = 0 which can beexpanded to give:x² - (p + q)x + pq = 0Which comparing ... = 2(It doesn't matter if the other prime is even (2) or not as itcancels out from a - b.)

Have you heard of the gender neutral honorific title Mx?

Description : Have you heard of the gender neutral honorific title Mx?

Last Answer : answer:I have heard of it. I am just not sure when to use it. And given that it took Ms. a good twenty years to be considered somewhat acceptable, but still not at all universal, I don’t see it becoming widespread very quickly. And, the use of honorifics is falling by the wayside.

What should I look for when buying a used Mazda MX-5 ?

Description : What should I look for when buying a used Mazda MX-5 ?

Last Answer : Not the test drive to worry about. Take it to a GOOD mechanic and have the engine examined.

Do Freehand Mx have a "dynamic textbox" feature like... in Master Pages?

Description : Do Freehand Mx have a "dynamic textbox" feature like... in Master Pages?

Last Answer : I’ve been asking around, and people who works in print told me that freehand DOES NOT have that feature. period. (thats what they said)

how can I report a sales fraud in Cozumel,MX

Description : how can I report a sales fraud in Cozumel,MX

Last Answer : Need Answer

In `y=mx+c`, make c as the subject.

Description : In `y=mx+c`, make c as the subject.

Last Answer : In `y=mx+c`, make c as the subject.

Tijuana, MX, Mexico?

Description : Tijuana, MX, Mexico?

Last Answer : Tijuana, MX has become synonymous with spontaneous trips southof the border. Unlike Cancun, another popular U.S. touristdestination, Tijuana is only a few miles from the Californiaborder. In fact, ... , and the Tijuana Dragons, who are part of the AmericanBasketball League.Tijuana has done its

If MN/MX is low the 8086 operates in ______ mode.

Description : If MN/MX is low the 8086 operates in  ______ mode.   (a) Minimum (b) Maximum (c) Minimum & Maximum (d) Medium 

Last Answer : If MN/MX is low the 8086 operates in  Maximum mode.