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5. Find the values of for which the following equations have real 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

and [After taking square root on both sides]

The value of can be represented as

(ii)

Solution:

Given,

It can be rewritten as,

It’s of the form of

Where,

For the given quadratic equation to have real roots

and

The value of should be greater than or equal to  to have real roots.