10. Find the values of p for which the quadratic equation has equal roots. Also, find the roots.

Quadratic is that type of problem which deals with a variable multiplied by itself – an operation known also as squaring.

Solution:

The given equation is in the form of

Where

For the equation to have real and equal roots, the condition is

⇒

⇒

⇒

⇒

Solving for p by factorization,

⇒

⇒

⇒

Either ⇒ Or, ⇒

So, the value of can either be or 

Now, using in the given quadratic equation we get

⇒

Thus, is the root of the given quadratic equation.

Next, on using in the given quadratic equation we get

⇒

Thus, ⇒ is the root of the given quadratic equation.