Question

If -5 is a root of the quadratic equation $2x^2+px-15=0$ and the quadratic equation $p(x^2+x)+k=0$ has equal roots. The value of k is ___.

• A. $\frac{7}{4}$
• B. $\frac{7}{2}$
• C. $\frac{7}{3}$
• D. $\frac{7}{5}$

Answer 1

Since -5 is a root of the equation $2x^2+px-15=0$.

Therefore, $2(-5{)}^2-5p-15=0$

$\Rightarrow 50-5p-15=0\Rightarrow 5p=35\Rightarrow p=7$

Putting p = 7 in $p(x^2+x)+k=0$, we get $7x^2+7x+k=0$

This equation will have equal roots, if

Discriminant $=0\Rightarrow 49-4\times 7\times k=0\Rightarrow k=\frac{49}{28}\Rightarrow k=\frac{7}{4}$