2. Find the values of for which the roots are real and equal in each of the following equations:

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

(xv)

Solution:

The given equation is in the form of

Where

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

⇒

⇒

⇒

⇒

Taking common,

⇒

Now, either ⇒ or ⇒

So, the value of can either be or 

(xvi)

Solution:

The given equation is in the form of

Where

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

⇒

⇒

⇒ [dividing by both sides]

⇒

Now, solving for by completing the square we have

⇒

⇒

⇒

⇒ or

So, the value of k can either be or