Table of contents  
Introduction  
Quadratic Formula Proof  
Nature of Roots of the Quadratic Equation  
Sum and Product of Roots of Quadratic Equation 
Quadratic Formula: The roots of a quadratic equation ax2 + bx + c = 0 are given by x = [b ± √(b2  4ac)]/2a.
Example: Let us find the roots of the same equation that was mentioned in the earlier section x^{2}  3x  4 = 0 using the quadratic formula.
a = 1, b = 3, and c = 4.
x = [b ± √(b^{2}  4ac)]/2a= [(3) ± √((3)^{2}  4(1)(4))]/2(1)
= [3 ± √25] / 2
= [3 ± 5] / 2
= (3 + 5)/2 or (3  5)/2
= 8/2 or 2/2
= 4 or 1 are the roots.
Discriminant: D = b^{2}  4ac
The following list of important formulas is helpful to solve quadratic equations.
Methods to Solve Quadratic Equations
Factorization of Quadratic Equation
Method of Completing the Square
Quadratic Equations Having Common Roots
Maximum and Minimum Value of Quadratic Expression
Maximum and Minimum Value of Quadratic Equation
The maximum and minimum values of the quadratic expressions are of further help to find the range of the quadratic expression: The range of the quadratic expressions also depends on the value of a. For positive values of a( a > 0), the range is [ F(b/2a), ∞), and for negative values of a ( a < 0), the range is (∞, F(b/2a)].
Note that the domain of a quadratic function is the set of all real numbers, i.e., (∞, ∞).
Some of the belowgiven tips and tricks on quadratic equations are helpful to more easily solve quadratic equations.
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1. What is a quadratic equation? 
2. How do you solve a quadratic equation using the quadratic formula? 
3. Can a quadratic equation have no real solutions? 
4. What is the discriminant of a quadratic equation? 
5. How do you find the sum and product of the roots of a quadratic equation? 

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