Question

If the roots of a quadratic equation are $\frac{p}{q},-\frac{q}{p}$, then the equation is:

• A. $q{x}^2-(q^2+p^2)x-pq=0$
• B. $pq{x}^2-(p^2-q^2)x-pq=0$
• C. $p{x}^2-(p^2+1)x+p=0$
• D. $p^2{x}^2-(p^2-q^2)x-pq=0$

Answer 1

Answer: (B)

$pq{x}^2-(p^2-q^2)x-pq=0$

(B) $\alpha +\beta =\frac{p}{q}-\frac{q}{p}=\frac{p^2-q^2}{pq}$
and $\alpha \beta =\left(\frac{p}{q}\right)-\left(\frac{q}{p}\right)=-1$
$=x^2-\left(\frac{p^2-q^2}{pq}\right)x-1=0$
or $pq{x}^2-(p^2-q^2)x-pq=0$