Question

If $x^2-1$ is a factor of $x^4+a{x}^3+3x-b$, then

• A. a = 3, b = –1
• B. a = –3, b = 1
• C. a = 3, b = 1
• D. None of these

Answer 1

The correct option is B a = –3, b = 1

$Letf\left(x\right)=x^4+a{x}^3+3x-b=0$
Then, f(1) = 0
$\Rightarrow a-b+4=0$ . . . . .(i)
and f(–1) = 0
$\Rightarrow a+b+2=0$ . . . . .(ii)
On solving Equations (i) and (ii), we get
a = – 3, b = 1