Question

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

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

Answer 1

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

Given that $p$ and $q$ are the roots of $x^2+px+q=0$

Then, using sum and product of roots, we have
$p+q=-p$

$2p=-q$ ....(i)

$pq=q$ ....(ii)

Putting the value of $q$ in equation (ii), we get

$p(-2p)=-2p$

$\Rightarrow 2p^2=2p$

$\Rightarrow p=1$

Substituting this value in equation (i), we get

$2\left(1\right)=-q$

$\Rightarrow q=-2$

Thus $p=1$ and $q=-2$.