Question

if (x+1) and(x-1) are factors of p(x) =ax^3+x^2-2x+b, find the value of a and b​

Answer 1

Given :

• (x + 1) and (x - 1) are factors of the polynomial ax³ + x² - 2x + b

To Find :

We have to find the value of a and b

Solution :

(x + 1) = 0

→ x = -1

Put x as -1 in the polynomial.

→ a(-1)³ + (-1)² - 2(-1) + b = 0

→ -a + 1 + 2 + b = 0

→ -a + b + 3 = 0 ........(1)

$\rule{150}{2}$

(x - 1) = 0

→ x = 1

Put x as -1 in the polynomial.

→ a(1)³ + (1)² - 2(1) + b = 0

→ a + 1 - 2 + b = 0

→ a + b - 1 = 0 ........(1)

$\rule{200}{2}$

From equation 1.

→ -a + b = -3

→ b = -3 + a

Put value of b in equation 2.

→ a + (-3 + a) - 1 = 0

→ a - 3 + a - 1 = 0

→ 2a = 4

→ a = 2

Put value of a in equation 1.

-2 + b + 3 = 0

→ 1 + b = 0

→ b = -1

Answer 2

Answer:

Step-by-step explanation:

a = 2 and b = -1