# What should be added to the polynomial so that it becomes perfect square 4X square plus 8X?

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#4x^2+8x#

##### 2 Answers

4

#### Explanation:

By adding four we can make it perfect square

Thus it becomes a perfect square

But how do we get to this answer without any guess , here's the role of discriminant.

Any quadratic equation is of form

Here , discriminant

For perfect squares it is

So , we get

That's the answer

#### Explanation:

A perfect square is of form:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the unknown value be

Set

Compare

Compare

Substituting for

Compare

Thus

Giving: