Question

If $x^2-3x+2$ is a factor of $x^4-a{x}^2+b$ then the equation whose roots are $a,b$ is

• A. $x^2+9x-20=0$
• B. $x^2-9x-20=0$
• C. $x^2+9x+20=0$
• D. $x^2-9x+20=0$

Answer 1

The correct option is D $x^2-9x+20=0$

$x^2-3x+2=(x-1)(x-2)$ is factor of $f\left(x\right)=x^4-a{x}^2+b$
So,$f\left(1\right)=0\text{and}f\left(2\right)=0$
$\Rightarrow 1-a+b=0\text{and}16-4a+b=0$
$\Rightarrow a=5,b=4$
$\therefore \text{Required equation:}{x}^2-(5+4)x+5.4=0$
$\Rightarrow x^2-9x+20=0$