Question

if both x+1 and x-1 are factors of ax3+x2-2x+b, find the values of a and b.

Answer 1

Let p(x) = ax3 + x2 - 2x + b

Since (x+1) and (x-1) are the factors of p(x),

∴ p(-1) = 0 and p(1) = 0

∴ p(-1) = a(-1)3 + (-1)2 - 2 (-1) + b = 0

⇒ - a + 1 + 2 + b = 0

⇒ a - b = 3 ---- (i)

Again, p(1) = a(1)3 + (1)2 - 2(1) + b = 0

⇒ a + 1 - 2 + b = 0

⇒ a + b = 1 ----- (ii)

solving equations (i) and (ii) we get a = 2 and b = -1

Hope this would help you