If both ( x + 1) and ( x - 1) are factors of ax 3 + x 2 - 2 x + b, find a and b.

Question

If both ( x + 1) and ( x - 1) are factors of  ax 3 + x 2 - 2 x + b, find a and b.

Philoid · Accepted Answer

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

If both (x + 1) and (x - 1) are factors of ax3 + x2 - 2x + b, find a and b.

If both (x + 1) and (x - 1) are factors of ax³ + x² - 2x + b, find a and b.