Question

(X+1) and(x-1) are factor of ax^3+x^2-2x+b. This question which book +

Answer 1

Answer:

a = 2 and b = 1

Step-by-step explanation:

If x + 1 and x - 1 are factors of ax^4 + ax^3+x^2-2x+b, value of this polynomial must be 0, for x = - 1 or x = 1.

For x = - 1:

= > ax^3 + x^2 - 2x + b = 0

= > a(-1)³ + (-1)² - 2(-1) + b = 0

= > a(-1) + (1) - 2(-1) + b = 0

= > - a + 1 + 2 + b = 0

= > a - b = 3 ... (1)

For x = 1:

= > ax^3 + x^2 - 2x + b = 0

= > a(1)³ + (1)² - 2(1) + b = 0

= > a(1) + (1) - 2(1) + b = 0

= > a + 1 - 2 + b = 0

= > a + b = 1 ... (2)

Adding (1) & (2):

= > (a + b) + (a - b) = 3 + 1

= > a + b + a - b = 4

= > 2a = 4

= > a = 2

Thus,

= > a - b = 1

= > 2 - b = 1

= > 2 - 1 = b

= > 1 = b