Question

If $x^2-4$ is a factor of $2x^3+a{x}^2+bx+12$ where a and b are constant Then values of a and b are

• A. -3, 8
• B. 3, 8
• C. -3, -8
• D. 3, -8

Answer 1

Answer: (C)

-3, -8

$x^2-4$ is a factor of $2x^3+a{x}^2+bx+12$
$x^2-4=0$
$\Rightarrow x=2$ and $x=-2$
$2x^3+a{x}^2+bx+12=0$ at $x=2$ and $x=-2$

By putting $x=2$ in given polynomial. we get
$\Rightarrow 2(2{)}^3+a(2{)}^2+b\left(2\right)+12=0$
$\Rightarrow 16+4a+2b+12=0$
$\Rightarrow 4a+2b=-28$ .......(1)

By putting $x=-2$ in given polynomial. we get
$\Rightarrow 2(-2{)}^3+a(-2{)}^2+b(-2)+12=0$
$\Rightarrow -16+4a-2b+12=0$
$\Rightarrow 4a-2b=4$ ........(2)

By adding (1) and (2) we get
$8a=-24$
$\Rightarrow a=-3$

Now, put a in (1) we get
$4(-3)+2b=-28$
$\Rightarrow 2b=-16$
$\Rightarrow b=-8$
Option C is correct.