If x2 –1 is a factor of x4 + ax3 + 3x – b then- | MATH - SOLUTION OF QUADRATIC INEQUATIONS AND MISCELLANEOUS EQUATIONS | SolveeIt | Solveeit

Today, August 19

Question

If x² –1 is a factor of x⁴ + ax³ + 3x – b then-

A

a = 3, b = –1

B

a = –3, b = 1

C

a = 3, b = 1

D

None of these

Answer

a = –3, b = 1

Explanation

Solution

Let f(x) = x⁴ + ax³ + 3x – b = 0

so, f(1) = 0 Q a – b + 4 = 0 …..(i)

and f(–1) = 0 ∴ a + b + 2 = 0 …. (ii)

on solving equation (i) and (ii),

a = –3, b = 1