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

<img src="ib mathematics tutors.png" alt="ib mathematics tutors>

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 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.

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