Question

If $f\left(x\right)=2x^4-7x^3+ax+b$ is divisible by $(x-1)$ and $(x-2)$, then $(a,b)=$

• A. $(19,-14)$
• B. $(19,14)$
• C. $(-19,14)$
• D. $(-19,-14)$

Answer 1

Answer: (A)

$(19,-14)$

$f\left(x\right)$ is divisible by $(x-1)$ and $(x-2)$
So, $f\left(1\right)=0$ and $f\left(2\right)=0$
$f\left(1\right)=2-7+a+b=a+b-5=0$
$\Rightarrow a+b=5$
$f\left(2\right)=32-56+2a+b=2a+b-24=0$
$\Rightarrow 2a+b=24$
From the above two relations, we have

$a=19$ and $b=-14$