Question

For what value(s) of p will the quadratic equation x^2+px+7=0 have equal roots?

Answer 1

Given

$x^2+px+7=0$

To find:

For what value(s) of p will the quadratic equation have equal roots?​

Explanation:

It is given that,

$x^2+px+7=0$

That implies,

Since the quadratic equation has equal roots.

Then,

$b^2-4ac=0$

From the quadratic equation,

$b=p,\text{ }a=1,\text{ }c=7$

Therefore,

$\begin{gathered} p^2-4\times1\times7=0 \\ p^2-28=0 \\ p^2=28 \\ p=\pm2\sqrt{7} \end{gathered}$

Hence, for p = 2√7 and p = -2√7 the given quadratic equation has equal roots.