# 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

x²+bx/a=-c/a

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

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

x²+bx/a+b²/4a² =-c/a²+b²/4a²

(x+b/2a)²=b²-4ac/4a²

now, take square root on both sides

x+b/2=±√b²-4ac/a²

x=-(b/2a)±√b²-4ac/2a

**x=-b±√b²-4ac/2a**

This formula is known as quadratic formula, we can put values of a, b and c from any equation and find the value of x (the variable) by directly using this formula.

IB Mathematics tutors can also explain the concept of conjugate roots with the help of quadratic formula. In a quadratic equation,

ax²+bx+c=0

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

These types of roots are called Conjugate Roots.

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.