Question

If $p,q$ are the roots of the equation $x^2+px+q=0$ then

• A. $p=-2,q=0$
• B. $p=0,q=1$
• C. $p=-2,q=1$
• D. $p=1,q=-2$

Answer 1

The correct option is D $p=1,q=-2$

Given : $x^2+px+q=0$
$p,q$ are roots
So,
Sum of roots, $S=p+q=-p$
And, Product of roots, $pq=q$
$\Rightarrow pq-q=0\Rightarrow q(p-1)=0$
$\Rightarrow q=0,p=1$
Now, if $q=0,thenp=0\Rightarrow p=q$
If $p=1,thenp+q=-p$
$\Rightarrow q=-2p\Rightarrow q=-2\times \left(1\right)=-2$
Hence, $p=1,q=-2$