3. In the following, determine the set of values of for which the given quadratic equation has real roots:

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

(iii)

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 roots.

(iv)

Solution:

Given,

It’s of the form of

Where,

For the given quadratic equation to have real roots

⇒

The given equation will have real roots if,

⇒ so,

The value of should not exceed to have real roots.