Question

if (x-2)(x+3)are factors of p(x)=x^3+ax^2+bx-20 then find the value of a and b​

Answer 1

Given :

• (x-2) , (x+3) are factors of p(x)=x³+ax²+bx-20

To Find :

• value of a and b​

Solution :

( x - 2 ) & ( x + 3 ) are factors of p(x)=x³+ax²+bx-20

⇒ 2 , - 3 are zeroes of the polynomial , p(x)=x³+ax²+bx-20

__________________________

⇒ p ( 2 ) = 0

⇒ (2)³ + a(2)² + b(2) - 20 = 0

⇒ 8 + 4a + 2b - 20 = 0

⇒ 4a + 2b - 12 = 0

⇒ 2a + b  = 6 ... (1)

Now ,

p (-3) = 0

⇒ (-3)³ + a(-3)² + b(-3) - 20 = 0

⇒ - 27 + 9a - 3b - 20 = 0

⇒ 9a - 3b = 47 ... (2)

Now , solve (2) + 3*(1) , we get ,

⇒ 9a - 3b + 3 ( 2a + b ) = 47 + 3 (6)

⇒ 9a - 3b + 6a + 3b = 65

⇒ 15a = 65

⇒ a = 13/3

sub. a value in (1) , we get ,

⇒ 2( 13/3 ) + b = 6

⇒ 26/3 + b = 6

⇒ b = -8/3