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?​

Step-by-step 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*1*7=0 \\ p^2-28=0 \\ p^2=28 \\ p=\pm2√(7) \end{gathered}`

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