Explain Factor Theorem : -Maths 9th

Explain Factor Theorem : -Maths 9th
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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x

Using factor theorem,show that (x-y) is a factor of x(y(square) - z(square)) + y(z(square) - x(square)) + z(x(square) - y(square) ) -Maths 9th

Description : Using factor theorem,show that (x-y) is a factor of x(y(square) - z(square)) + y(z(square) - x(square)) + z(x(square) - y(square) ) -Maths 9th

Last Answer : Solution :-

Using factor theorem, factorise the polynomial x3 + x2 - 4x - 4. -Maths 9th

Description : Using factor theorem, factorise the polynomial x3 + x2 - 4x - 4. -Maths 9th

Last Answer : Solution :-

Explain Remainder Theorem. -Maths 9th

Description : Explain Remainder Theorem. -Maths 9th

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Explain Apollonius' Theorem. -Maths 9th

Description : Explain Apollonius' Theorem. -Maths 9th

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Theorem 9.1 proof.Need it it urgently!!!!! -Maths 9th

Description : Theorem 9.1 proof.Need it it urgently!!!!! -Maths 9th

Last Answer : can you tell theorm name and of which lesson

About triangle and use of mid point theorem in it -Maths 9th

Description : About triangle and use of mid point theorem in it -Maths 9th

Last Answer : A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ∆ABC. A midpoint is a point on a line ... shown using this symbol ||. You also know the line segment is one-half the length of the third side.

By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Description : By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Last Answer : Find the remainder when p(x) is divided by g(x)

Theorem 9.1 proof.Need it it urgently!!!!! -Maths 9th

Description : Theorem 9.1 proof.Need it it urgently!!!!! -Maths 9th

Last Answer : can you tell theorm name and of which lesson

About triangle and use of mid point theorem in it -Maths 9th

Description : About triangle and use of mid point theorem in it -Maths 9th

Last Answer : A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ∆ABC. A midpoint is a point on a line ... shown using this symbol ||. You also know the line segment is one-half the length of the third side.

By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Description : By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Last Answer : Find the remainder when p(x) is divided by g(x)

BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

Description : BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

Last Answer : NEED ANSWER

BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

Description : BY REAMINDER THEOREM FIND THE REAMINDER, WHEN P(x) IS DIVIDED BY G(X), WHERE -Maths 9th

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Define : Addition Theorem of Probability. -Maths 9th

Description : Define : Addition Theorem of Probability. -Maths 9th

Last Answer : (a) For Two Events. If A and B are two events associated with a random experiment, then P(A ∪ B) = P(A) + P(B) - P(A ∩ B) ⇒ P(A or B) = P(A) + P(B) - P(A and B) Corollary 1: If A and B are ... that A ⊆ B, then P(A) ≤ P(B) (ii) If E is an event associated with a random experiment, then 0 P(E) ≤ 1

Define : Multiplication Theorem on Probability. -Maths 9th

Description : Define : Multiplication Theorem on Probability. -Maths 9th

Last Answer : Statement I. If two events A and B are independent, then probability that they will both occur is equal to the product of their individual probabilities. i.e. P (A and B) = P (A) P (B) ... occurrence of two independent events. Method. Use the relation P (A ∩ B) = P (A) . P (B).

isosceles triangle theorem -Maths 9th

Description : isosceles triangle theorem -Maths 9th

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isosceles triangle theorem -Maths 9th

Description : isosceles triangle theorem -Maths 9th

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Without using Pythagoras’ theorem, show that the points A (0, 4), B(1, 2) and C(3, 3) are the vertices of a right angle triangle. -Maths 9th

Description : Without using Pythagoras’ theorem, show that the points A (0, 4), B(1, 2) and C(3, 3) are the vertices of a right angle triangle. -Maths 9th

Last Answer : Slope (m) = \(rac{(y_2-y_1)}{(x_2-x_1)}\) = \(rac{6-2}{5-1}\) = \(rac{4}{4}\) = 1Also slope (m) = tan θ, where θ is the inclination of the line to the positive direction of the x-axis in the anticlockwise direction. tan θ = 1 ⇒ θ = tan –11 = 45º.

Determine which of the following polynomials has (x + 1) a factor: (i) x3+x2+x+1 -Maths 9th

Description : Determine which of the following polynomials has (x + 1) a factor: (i) x3+x2+x+1 -Maths 9th

Last Answer : Solution: Let p(x) = x3+x2+x+1 The zero of x+1 is -1. [x+1 = 0 means x = -1] p(−1) = (−1)3+(−1)2+(−1)+1 = −1+1−1+1 = 0 ∴By factor theorem, x+1 is a factor of x3+x2+x+1

3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Description : 3. Check whether 7+3x is a factor of 3x3+7x. -Maths 9th

Last Answer : Solution: 7+3x = 0 ⇒ 3x = −7 ⇒ x = -7/3 ∴Remainder: 3(-7/3)3+7(-7/3) = -(343/9)+(-49/3) = (-343-(49)3)/9 = (-343-147)/9 = -490/9 ≠ 0 ∴7+3x is not a factor of 3x3+7x

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e , show that a + c + e = b + d = 0. -Maths 9th

Description : If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e , show that a + c + e = b + d = 0. -Maths 9th

Last Answer : Since x2 - 1 = (x - 1) is a factor of p(x) = ax4 + bx3 + cx2 + dx + e ∴ p(x) is divisible by (x+1) and (x-1) separately ⇒ p(1) = 0 and p(-1) = 0 p(1) = a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0 ... (b+d) = 0 ⇒ b + d = 0 ---- (iii) comparing equations (ii) and (iii) , we get a + c + e = b + d = 0

√3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Description : √3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

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If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Description : Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

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Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our answer

Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Description : Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Last Answer : This answer was deleted by our moderators...

Show that p-1 is a factor of p10 -1 and also of p11 -1. -Maths 9th

Description : Show that p-1 is a factor of p10 -1 and also of p11 -1. -Maths 9th

Last Answer : Let g (p) = p10 -1 and h(p) = p11 -1. On putting p=1 in Eq. (i), we get g(1)=110-1= 1-1=0 Hence, p-1 is a factor of g(p). Again, putting p = 1 in Eq. (ii), we get h (1) = (1)11 -1 = 1 -1 = 0 Hence, p -1 is a factor of h(p).

If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Description : If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Last Answer : Let p(x) = a5 -4a2x3 +2x + 2a +3 Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 ⇒ -32a5 + 32a5 -4a + 2a+ 3 = 0 ⇒ -2a + 3 = 0 2a =3 a = 3/2. Hence, the value of a is 3/2.

Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Description : Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Last Answer : Solution of this question

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Description : Show that x + a is a factor of xn + an for any odd +ve integer n. -Maths 9th

Last Answer : Let f(x) = xn + an x + a will be the factor of xn + an if f(-a) = 0 Now f(-a) = (-a)n + an = 0 (since n is a odd +ve integer) Thus (x +a) is a factor of xn + an .

If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e , show that a + c + e = b + d = 0. -Maths 9th

Description : If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e , show that a + c + e = b + d = 0. -Maths 9th

Last Answer : Since x2 - 1 = (x - 1) is a factor of p(x) = ax4 + bx3 + cx2 + dx + e ∴ p(x) is divisible by (x+1) and (x-1) separately ⇒ p(1) = 0 and p(-1) = 0 p(1) = a(1)4 + b(1)3 + c(1)2 + d(1) + e = 0 ... (b+d) = 0 ⇒ b + d = 0 ---- (iii) comparing equations (ii) and (iii) , we get a + c + e = b + d = 0

√3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Description : √3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Last Answer : This answer was deleted by our moderators...

If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Description : If x + 1 is a factor of the polynomial 2x2 + kx, then the value of k is -Maths 9th

Last Answer : (c) Let p(x) = 2x2 + kx Since, (x + 1) is a factor of p(x), then p(-1)=0 2(-1)2 + k(-1) = 0 ⇒ 2-k = 0 ⇒ k= 2 Hence, the value of k is 2.

x + 1 is a factor of the polynomial -Maths 9th

Description : x + 1 is a factor of the polynomial -Maths 9th

Last Answer : (b) Let assume (x + 1) is a factor of x3 + x2 + x+1. So, x = -1 is zero of x3 + x2 + x+1 (-1)3 + (-1)2 + (-1) + 1 = 0 ⇒ -1+1-1 + 1 = 0 ⇒ 0 = 0 Hence, our assumption is true.

Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Description : Which of the following is a factor of (x+ y)3 – (x3 + y3) ? -Maths 9th

Last Answer : This answer was deleted by our moderators...

Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Description : Show that, x + 3 is a factor of 69 + 11c – x2 + x3 -Maths 9th

Last Answer : This answer was deleted by our moderators...

Determine which of the following polynomial has x – 2 a factor -Maths 9th

Description : Determine which of the following polynomial has x – 2 a factor -Maths 9th

Last Answer : first option is the correct answer for the given question solution is as follows:- let x-2=0 then, x=2 put x in (i) 3(2)(2)+6(2)-24=0 12+12-24=0 {use BODMAS rule for solution}... 24-24=0 0=0 this verifies our answer

Show that p-1 is a factor of p10 -1 and also of p11 -1. -Maths 9th

Description : Show that p-1 is a factor of p10 -1 and also of p11 -1. -Maths 9th

Last Answer : Let g (p) = p10 -1 and h(p) = p11 -1. On putting p=1 in Eq. (i), we get g(1)=110-1= 1-1=0 Hence, p-1 is a factor of g(p). Again, putting p = 1 in Eq. (ii), we get h (1) = (1)11 -1 = 1 -1 = 0 Hence, p -1 is a factor of h(p).

If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Description : If x + 2a is a factor of a5 -4a2x3 +2x + 2a +3, then find the value of a. -Maths 9th

Last Answer : Let p(x) = a5 -4a2x3 +2x + 2a +3 Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 ⇒ -32a5 + 32a5 -4a + 2a+ 3 = 0 ⇒ -2a + 3 = 0 2a =3 a = 3/2. Hence, the value of a is 3/2.

Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Description : Find the value of m, so that 2x -1 be a factor of 8x4 +4x3 -16x2 +10x+07. -Maths 9th

Last Answer : Solution of this question

If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Description : If x +1 is a factor of ax3 +x2 -2x + 4a - 9, then find the value of a. -Maths 9th

Last Answer : The value of a

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : Let f(x)=xn+an. In order to prove that x+a is a factor of f(x) for any odd positive integer n, it is sufficient to show that f(−a)=0. f(−a)=(−a)n+an=(−1)nan+an f(−a)=(−1+1)an [ n is odd positive integer ] f(−a)=0×an=0 Hence, x+a is a factor of xn+an, when n is an odd positive integer.

Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Description : Show that x+a is a factor of x^n+a^n for any odd positive n -Maths 9th

Last Answer : This answer was deleted by our moderators...

If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

Description : If x+1 is a factor of the polynomial 3x(square) - kx,then find the value of k. -Maths 9th

Last Answer : Solution :-

Find the value of k,if y+3 is a factor of 3y(to the power square) + ky + 6. -Maths 9th

Description : Find the value of k,if y+3 is a factor of 3y(to the power square) + ky + 6. -Maths 9th

Last Answer : Solution :-

Find the value of a, if x-a is a factor of x(cube) - ax(square) + a-1. -Maths 9th

Description : Find the value of a, if x-a is a factor of x(cube) - ax(square) + a-1. -Maths 9th

Last Answer : Solution :-

If x(square) - 1 is a factor of ax(cube) + bx(square) + cx + d,show that a+c=0. -Maths 9th

Description : If x(square) - 1 is a factor of ax(cube) + bx(square) + cx + d,show that a+c=0. -Maths 9th

Last Answer : Solution :-