Question

If $p$ and $q$ are rational, then uncommon root of the equation $x^2-px+2q=0$ is equal to

• A. $-q$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{-1}{2}$

Answer 1

The correct option is A $-q$

$x^2-px+2q=0.........\left(i\right)$
$x^2-qx+2p=0...........\left(ii\right)$
$subtracting\left(ii\right)from\left(i\right)$
$x(q-p)+2(q-p)=0$
$\Rightarrow (q-p)(x+2)=0$
$Hence$
$x=-2isthecommonroot$
$Substitutingweget$
$4+2p+2q=0$
$\Rightarrow 2(p+q)=-4$
$\Rightarrow p+q=-2$
$Hencetheequationbecomes$
$x^2+(q+2)x+2q=0$
$\Rightarrow (x+q)(x+2)=0$
$Henceuncommonrootisx=-q$