## How to Prove quadratic formula?

Many ib mathematics tutors consider quadratic equations as one of the most important topics of ib maths. There are following ways to solve a quadratic equation

**► Factorization method**

**►complete square method**

**► graphical method**

**► Quadratic formula method**

The quadratic formula is the strongest method to solve a quadratic equation. In this article, I will use …… steps to prove the quadratic formula

Given equation: ax²+bx+c=0

**Step-1:** transfer constant term to right side

ax²+bx=-c

**Step-2:** divide both sides by coefficient of x²

**Step-3:**write (coefficient of x/2)² that is (b/2a)²=b²/4a²

**Step-4:**Add this value to both sides

**x=-b±√b²-4ac/2a**

if a, b and c are all rational numbers and one root of the quadratic equation is

**a+√b**then the second root will automatically become a-√b. that can be understood easily as we use one +ve and one -ve sign in quadratic formula.

These types of roots are called Conjugate Roots.