Question

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

• A. $\frac{7}{4}$
• B. $\frac{7}{2}$
• C. $-\frac{7}{4}$
• D. None of these

Answer 1

Answer: (A)

$\frac{7}{4}$

$-5$ is root of $2x^2+px-15=0$

So $2{\left(-5\right)}^2+p\left(-5\right)-15=0$

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

$\Rightarrow 5p=35$

$\Rightarrow p=7$

Now $p\left(x^2+x\right)+k=0$

Becomes $7x^2+7x+k=0$

If this has equal root

Then $b^2-4ac=0$

$\Rightarrow 7^2-4\times 7\times k=0$

$\Rightarrow 7=4k$

$\Rightarrow k=\frac{7}{4}$