Question

If x -1 and x + 2 are factors of x3+10x2+ ax+b, then find the values of a and b.

Answer 1

EXPLANATION.

x - 1 and x + 2 are the factor of the equation.

⇒ x³ + 10x² + ax + b.

As we know that,

⇒ x - 1 is a factor of polynomial.

⇒ x - 1 = 0.

⇒ x = 1.

Put the value of x = 1 in equation, we get.

⇒ (1)³ + 10(1)² + a(1) + b = 0.

⇒ 1 + 10 + a + b = 0.

⇒ 11 + a + b = 0.

⇒ b = - 11 - a. - - - - - - (1).

⇒ x - 2 is a factor of polynomial.

⇒ x - 2 = 0.

⇒ x = 2.

Put the value of x = 2 in equation, we get.

⇒ (2)³ + 10(2)² + a(2) + b = 0.

⇒ 8 + 10(4) + 2a + b = 0.

⇒ 8 + 40 + 2a + b = 0.

⇒ 48 + 2a + b = 0. - - - - - (2).

Put the value of equation (1) in equation (2), we get.

⇒ 48 + 2a + [- 11 - a] = 0.

⇒ 48 + 2a - 11 - a = 0.

⇒ 37 + a = 0.

⇒ a = -37.

Put the value of a = -37 in equation (1), we get.

⇒ b = - 11 - a.

⇒ b = - 11 - (-37).

⇒ b = - 11 + 37.

⇒ b = 26.

Values of A = -37 & B = 26.

Answer 2

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EXPLANATION.

x - 1 and x + 2 are the factor of the equation.

⇒ x³ + 10x² + ax + b.

As we know that,

⇒ x - 1 is a factor of polynomial.

⇒ x - 1 = 0.

⇒ x = 1.

Put the value of x = 1 in equation, we get.

⇒ (1)³ + 10(1)² + a(1) + b = 0.

⇒ 1 + 10 + a + b = 0.

⇒ 11 + a + b = 0.

⇒ b = - 11 - a. - - - - - - (1).

⇒ x - 2 is a factor of polynomial.

⇒ x - 2 = 0.

⇒ x = 2.

Put the value of x = 2 in equation, we get.

⇒ (2)³ + 10(2)² + a(2) + b = 0.

⇒ 8 + 10(4) + 2a + b = 0.

⇒ 8 + 40 + 2a + b = 0.

⇒ 48 + 2a + b = 0. - - - - - (2).

Put the value of equation (1) in equation (2), we get.

⇒ 48 + 2a + [- 11 - a] = 0.

⇒ 48 + 2a - 11 - a = 0.

⇒ 37 + a = 0.

⇒ a = -37.

Put the value of a = -37 in equation (1), we get.

⇒ b = - 11 - a.

⇒ b = - 11 - (-37).

⇒ b = - 11 + 37.

⇒ b = 26.

Values of A = -37 & B = 26.

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