What is the meaning of solving a quadratic equation?

Suppose, we have quadratic equation which is in the standard form . We want to find value of such that left hand side becomes equal to right hand side which is 0.

For example, we have **Quadratic Equation**

Putting in **Quadratic Equation, **we get left hand side equal to

Therefore, L.H.S = R.H.S. It means is one of the solutions of the quadratic equation **.**

Putting x = 3 in equation, we get left hand side equal to

Therefore, L.H.S = R.H.S. It means is another solution of the quadratic equation **.**

We can here say that are solutions of the **Quadratic Equation** .

Solutions of any **Quadratic Equation** are also called **roots** of the **Quadratic Equation**.

**How can we find roots of the Quadratic Equation by Factorization?**

Suppose, we are given a **Quadratic Equation **of the form where, .

We can factorize this equation through middle term which is . We split middle term into two terms in such a way that product of terms becomes equal to .

For example, we have equation

In this equation, we have

Therefore, we split middle term into two terms which are and because their product is equal to . Remember that, we also need ().

Following the process, we can say that

, or

Lets take another example, Find value of in **Quadratic Equation**.

We split the middle term into two terms such that their product become equal to .

If, you cannot figure out directly what are the terms which make product equal to then start trying different combinations of splitting.

{Product of terms ( and ) is not equal to }

{Product of terms ( and ) is not equal to }

{Product of terms ( and ) is not equal to }

**{Product of terms ( and ) is equal to }, **Therefore, we consider this combination.

, or