For which value of `p` among the following, does the quadratic equation `3x^(2) + px + 1 = 0` have real roots ?

For which value of `p` among the following, does the quadratic equation `3x^(2) + px + 1 = 0` have real roots ?
by

1 Answer

Answer :

For which value of `p` among the following, does the quadratic equation `3x^(2) + px + 1 = 0` have real roots ?
by

Related questions

If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Description : If p, q, r are positive and are in A.P., the roots of quadratic equation px^2 + qx + r = 0 are real for : -Maths 9th

Last Answer : Given p,q,r are in A.P. then q=2p+r​.....(1). Now px2+qx+r=0 will have real root then q2−4pr≥0. or, 4(p+r)2​−4pr≥0 or, p2+r2−14pr≥0 or, r2−14rp+49p2≥48p2 or, (r−7p)2≥(43​p)2 or, (pr​−7)2≥(43​)2 [ Since p=0 for the given equation to be quadratic] or, ∣∣∣∣∣​pr​−7∣∣∣∣∣​≥43​.

Find the value of m for which the quadratic equation , `3x^(2) + 10x + (m-3) = 0` has roots which are reciproal to each other.

Description : Find the value of m for which the quadratic equation , `3x^(2) + 10x + (m-3) = 0` has roots which are reciproal to each other.

Last Answer : Find the value of m for which the quadratic equation , `3x^(2) + 10x + (m-3) = 0` has roots which are reciproal to each other.

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 `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) = "_____"`.

A quadratic equation whose roots are 2 moe than the roots of the quadratic equation `2x^(2) +3x + 5 = 0`, can be obtained by substituting `"_____"` fo

Description : A quadratic equation whose roots are 2 moe than the roots of the quadratic equation `2x^(2) +3x + 5 = 0`, can be obtained by substituting `"_____"` fo

Last Answer : A quadratic equation whose roots are 2 moe than the roots of the quadratic equation `2x^(2) +3x + 5 = 0`, can be ... `"_____"` for x. `[(x-2)//(x+2)]`

Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Description : Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Last Answer : Let αα and ββ be the roots of the quadratic equation x2+px+q=0x2+px+q=0 Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., a product of roots ... 1 Now, from Eqs. (ii) and (iii), we get α=−3 and β=−4α=−3 and β=−4 which are correct roots.

Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Description : Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Last Answer : answer:

If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Description : If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Last Answer : answer:

If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.

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]

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 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.

In quadratic equation ax^2 + bx + c = 0 , Identities the sum and product of Roots? -Maths 9th

Description : In quadratic equation ax^2 + bx + c = 0 , Identities the sum and product of Roots? -Maths 9th

Last Answer : If the two roots of the quadratic equation ax2 + bx + c = 0 obtained by the quadratic formula be denoted by a and b, then we have α = \(\frac{-b+\sqrt{b^2-4ac}}{2a},\) β = \(\frac{-b-\sqrt{b^2-4ac}}{2a}\) ∴ Sum of roots ... then α + β = - (- \(\frac{5}{6}\)) = \(\frac{5}{6}\), ab = \(\frac{7}{6}\).

What are the roots of the quadratic equation a^2 b^2 x^2 – (a^2 + b^2)x + 1 = 0 ? -Maths 9th

Description : What are the roots of the quadratic equation a^2 b^2 x^2 – (a^2 + b^2)x + 1 = 0 ? -Maths 9th

Last Answer : answer:

The quadratic equation whose roots are three times the roots of 3ax^2 + 3bx + c = 0 is -Maths 9th

Description : The quadratic equation whose roots are three times the roots of 3ax^2 + 3bx + c = 0 is -Maths 9th

Last Answer : answer:

The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is 16. The least common multiple of the two

Description : The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is 16. The least common multiple of the two

Last Answer : The quadratic equation `x^2-1088x+295680=0` has two positive integral roots whose greatest common divisor is ... A. 18240 B. 18480 C. 18960 D. 19240

Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

Description : Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

Last Answer : Find the roots of quadratic equation `ax^(2) + (a-b + c) x - b +c = 0`.

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 `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))`

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 = "_____"`.

Explain Nature of Roots of a quadratic equation. -Maths 9th

Description : Explain Nature of Roots of a quadratic equation. -Maths 9th

Last Answer : answer:

If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

Description : If the sum as well as the product of roots of a quadratic equation is 9, then the equation is: -Maths 9th

Last Answer : answer:

Find the quadratic equation in x whose roots are `(-7)/(2)` and `(8)/(3)`.

Description : Find the quadratic equation in x whose roots are `(-7)/(2)` and `(8)/(3)`.

Last Answer : Find the quadratic equation in x whose roots are `(-7)/(2)` and `(8)/(3)`.

The quadratic equation having roots `-a,-b` is `"_____"`.

Description : The quadratic equation having roots `-a,-b` is `"_____"`.

Last Answer : The quadratic equation having roots `-a,-b` is `"_____"`.

If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

Description : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

Last Answer : If the roots of a quadratic equation `ax^(2) + bx + c` are complex, then `b^(2) lt "____"`

If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

Description : If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

Last Answer : If the roots of quadratic equation are equal , then the discriminant of the equation is `"______"`

The value of quadratic polynomial f (x) = 2x 2 – 3x- 2 at x = -2 is ...... (a) 12 (b) 15 (c) -12 (d) 16

Description : The value of quadratic polynomial f (x) = 2x 2 – 3x- 2 at x = -2 is ...... (a) 12 (b) 15 (c) -12 (d) 16

Last Answer : (a) 12

If one zero of the quadratic polynomial x 2 + 3x + k is 2, then the value of k is (a) 10 (b) –10 (c) 5 (d) –5

Description : If one zero of the quadratic polynomial x 2 + 3x + k is 2, then the value of k is (a) 10 (b) –10 (c) 5 (d) –5

Last Answer : (b) –10

The equation whose roots are the negatives of the roots of the equation x^7 + 3x^5 + x^3 – x^2 + 7x + 2 = 0 is : -Maths 9th

Description : The equation whose roots are the negatives of the roots of the equation x^7 + 3x^5 + x^3 – x^2 + 7x + 2 = 0 is : -Maths 9th

Last Answer : answer:

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:

`x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ,x_2 ,x_3 , x_4` form in increasing `GP`.,

Description : `x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ,x_2 ,x_3 , x_4` form in increasing `GP`.,

Last Answer : `x_1 ,x_2` are the `x^2-3x+A= 0; x_3 , x_4` are roots of the equation `x^2-12x + B =0` of the equation `x_1 ... x_(1) + x_(3) =5` D. `x_(2)+x_(4)=10`

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 ?

The roots of the equation `3x^(2) - 4sqrt(3x) + 4 = 0` are

Description : The roots of the equation `3x^(2) - 4sqrt(3x) + 4 = 0` are

Last Answer : The roots of the equation `3x^(2) - 4sqrt(3x) + 4 = 0` are

The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

Description : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

Last Answer : The roots of the equation `2x^(2) + 3x + c = 0` (where `x lt 0`) could be `"______"`.

For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

Description : For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

Last Answer : For the equation `2x^(2) - 3x + 5 = 0` sum of the roots is `"______"`.

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 = "______"`.

For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th

Description : For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th

Last Answer : answer:

Find minimum value of `px+qy` where `p>0, q>0, x>0, y>0` when `xy=r,^2` without using derivatives.

Description : Find minimum value of `px+qy` where `p>0, q>0, x>0, y>0` when `xy=r,^2` without using derivatives.

Last Answer : Find minimum value of `px+qy` where `p>0, q>0, x>0, y>0` when `xy=r,^2` without using ... `pqsqrtr` B. `2pqsqrtr` C. `2rsqrtpq` D. None of these

Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x – 2x = (- 2) (3-x) (iii) (x – 2) (x + 1) = (x – 1) (x + 3) (iv) (x – 3) (2x + 1) = x (x + 5) (v) (2x – 1) (x – 3) = (x + 5) (x – 1) (vi) x2 + 3x + 1 = (x – 2)2 (vii) (x + 2)3 = 2x(x2 – 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Description : Check whether the following are quadratic equations: (i) (x+ 1)2=2(x-3) (ii) x - 2x = (- 2) (3-x) (iii) (x - 2) (x + 1) = (x - 1) (x + 3) (iv) (x - 3) (2x + 1) = x (x + 5) (v) (2x - 1) (x - 3) = (x ... vi) x2 + 3x + 1 = (x - 2)2 (vii) (x + 2)3 = 2x(x2 - 1) (viii) x3 -4x2 -x + 1 = (x-2)3 -Maths 10th

Last Answer : this is the correct answer!

If the polynomial x^6 + px^5 + qx^4 – x^2 – x – 3 is divisible by x^4 – 1, then the value of p^2 + q^2 is : -Maths 9th

Description : If the polynomial x^6 + px^5 + qx^4 – x^2 – x – 3 is divisible by x^4 – 1, then the value of p^2 + q^2 is : -Maths 9th

Last Answer : The divisor is x4−1=(x−1)(x+1)(x2+1) By factor theorem, f(1)=f(−1)=0 Thus, 1+p+q−1−1−3=0 and 1+q−1−3=p−1 i.e., p+q=4 and p−q=−2 Adding the two, 2p=2 i.e. p=1 and ∴ q=3. ∴ p2+q2=1+9=10

If α , β are the zeroes of f(x) = px 2 – 2x + 3p and α + β = αβ then the value of p is: (a) 1/3 (b) -2/3 (c) 2/3 (d) -1/3

Description : If α , β are the zeroes of f(x) = px 2 – 2x + 3p and α + β = αβ then the value of p is: (a) 1/3 (b) -2/3 (c) 2/3 (d) -1/3

Last Answer : (c) 2/3

Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

Description : Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

Last Answer : Find the sum of the value (s) of a so that the equation (`x^(2) + 2ax + 2a + 3`) (`x^(2) + 2ax + 4a +5 `) = 0 has only 3 real distinct roots.

Find the slope of the line whose equation is px - qy = r + 1.?

Description : Find the slope of the line whose equation is px - qy = r + 1.?

Last Answer : 7

Let x,y,z be real numbers such that 3x, 4y and 5z from a geometric progression while x,y,z form an H.P. If the value of `((x)/(z) +(z)/(x))` can be ex

Description : Let x,y,z be real numbers such that 3x, 4y and 5z from a geometric progression while x,y,z form an H.P. If the value of `((x)/(z) +(z)/(x))` can be ex

Last Answer : Let x,y,z be real numbers such that 3x, 4y and 5z from a geometric progression while x,y,z form an H.P. If ... value equal to A. 29 B. 39 C. 49 D. 59

Of the following quadratic equations, which is the one whose roots are 2 and – 15 ? -Maths 9th

Description : Of the following quadratic equations, which is the one whose roots are 2 and – 15 ? -Maths 9th

Last Answer : answer:

If -√5 and √5 are the roots of the quadratic polynomial. Find the quadratic polynomial. (a) x-5 (b) (x-5)(x+5) (c) x 2 – 5 (d) x 2 – 25

Description : If -√5 and √5 are the roots of the quadratic polynomial. Find the quadratic polynomial. (a) x-5 (b) (x-5)(x+5) (c) x 2 – 5 (d) x 2 – 25

Last Answer : (c) x 2 – 5

If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

Description : If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

Last Answer : If one root of the quadratic equation `ax^(2) + bx + c = 0` is `15 + 2sqrt(56)` and `a,b` and c are rational, then find the quadratic equation.

If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

Description : If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

Last Answer : If `x = 1` is a solution of the quadratic equation `ax^(2) - bx + c = 0`, then b is equal to `"_______"`.

In the quadratic equation ax2 plus bx plus c 0 if b2 - 4ac?

Description : In the quadratic equation ax2 plus bx plus c 0 if b2 - 4ac?

Last Answer : If you mean b^2 -4ac then it is the discriminant of a quadraticequation.If the discriminant equals 0 then the equation has 2 equalroots.If the discriminant is greater than 0 then the equation has 2different roots.If the discriminant is less than 0 then it has no realroots.