Question

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

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

Answer 1

Answer: (B)

Let $f(x)=x^4-a x^2+b$
and $g(x)=x^2-3 x+2=(x-1)(x-2)$
$\because g(x)$ is a factor of $f(x)$
$\Rightarrow(x-1)$ and $(x-2)$ are factors of $f(x)$
$\therefore f(1)=0$ and $f(2)=0$ [by factor theorem]
$\Rightarrow 1-a+b=0$ and $16-4 a+b=0$
Solving above equations, we have
$a=5, b=4$
Equation whose roots are ' $a$ ' and ' $b$ ' is
$x^2-(a+b) x+a b=0$
or $x^2-9 x+20=0$