Question

If the sum of the roots of the quadratic equations is $1$ and sum of the squares of the roots is $13$, then find that equation

• A. $x^{2}+x-6=0$
• B. $x^{2}-x+6=0$
• C. $x^{2}-x-6=0$
• D. $x^{2}+x+6=0$

Answer 1

Answer: (C)

Let the roots of the quadratic equation are $\alpha$ and $\beta$ then it is given that
$\alpha+\beta=1$ and $\alpha^{2}+\beta^{2}=13$
$\therefore \alpha \beta=\frac{1}{2}\left[(\alpha+\beta)^{2}-\left(\alpha^{2}+\beta^{2}\right)\right]$
$=\frac{1}{2}[1-13]=-6$
So, equation of required quadratic is
$x^{2}-(\alpha+\beta) x+\alpha \beta=0$
$\Rightarrow x^{2}-x-6=0$