Question

If $4x^4-12x^3+x^{{}^2}+3ax-b$ is divided by $x^2-1$ then a = _______, and b=______

• A. $5,4$
• B. $4,9$
• C. $4,5$
• D. $1,-1$

Answer 1

Answer: (C)

$4,5$

$x^2-1=0\Rightarrow x=\pm 1$

Given a polynomial $P\left(x\right)={4x}^4-12x^3+x^2+3ax-b$

Using remainder theorem,as $P\left(x\right)$ is completely divisible by $x^2-1$

$\therefore P(\pm 1)=0\therefore P\left(1\right)=0\Rightarrow 4-12+1+3a-b=0\Rightarrow 3a-b=7\therefore P(-1)=0\Rightarrow 4+12+1-3a-b=0\Rightarrow 3a+b=17$

By soling both we get

$a=4$ ;$b=5$