Question

The roots of the equation $x^2+kx-12=0$ will differ by unity only, when

• A. $k=\pm \sqrt{12}$
• B. $k=\pm \sqrt{48}$
• C. $k=\pm \sqrt{47}$
• D. $k=\pm \sqrt{49}$

Answer 1

The correct option is D $k=\pm \sqrt{49}$

$k^2+kx-12=0$
$a,a+1$ are the roots. Therefore,
$2a+1=-k$
or $a=\frac{-k-1}{2}$
Also, $a^2+a=-12$
or $\frac{(k+1{)}^2}{4}-\frac{(k+1)}{2}=-12$
or $(k+1{)}^2+2(k+1)=-48$
or $(k+1{)}^2+2(k+1)+48=0$
or $(k+1-8)(k+1+6)=0$
or $(k-7)(k+7)=0$