6. Find the values of for which the given quadratic equation has real and distinct roots.

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

(i)

Solution:

Given,

It’s of the form of

Where,

For the given quadratic equation to have real roots

⇒

⇒

⇒

The value of should be lesser than  to have real and distinct roots.

(ii)

Solution:

Given,

It’s of the form of

Where,

For the given quadratic equation to have real roots

⇒

⇒

⇒

The value of should be lesser than  to have real and distinct roots.