Question

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

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

Answer 1

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

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

then $p+q=-p$ ....$\left(1\right)$

and $pq=q\Rightarrow pq-q=0\Rightarrow q(p-1)=0$ ....$\left(2\right)$

From $\left(2\right)$, we get $q=0$ or $p=1$ ...$\left(3\right)$

If $q=0$, then substituting it in equation $\left(1\right)$,

$p=-p\Rightarrow p=0$, which is not possible as $p$ and $q$ are distinct.

$\therefore p=1$ ....$[$from $\left(3\right)]$

$\Rightarrow 1+q=-1$ ....$[$from $\left(1\right)]$

$\Rightarrow q=-2$