Question

If the roots of $x^2-17x+16=0$ are $p,q$, then which of the following can be the equation with the roots $\frac{1}{\sqrt{p}},\frac{1}{\sqrt{q}}?$

• A. $x^4-17x^2-16=0$
• B. $16x^4+17x^2+16=0$
• C. $16x^4-17x^2+1=0$
• D. $x^4+17x^2+16=0$

Answer 1

The correct option is C $16x^4-17x^2+1=0$

Given that the roots of $x^2-17x+16=0$ are $p,q$
Here $a=1,b=-17,c=16$

We know that for
$a{x}^2+bx+c=0,a\ne 0$ with roots $\alpha ,\beta$
the transformed quadratic equation with roots $\frac{1}{\sqrt{\alpha }}\&\frac{1}{\sqrt{\beta }}$ is given by:
$c(x^2{)}^2+b(x{)}^2+a=0\Rightarrow 16x^4-17x^2+1=0$