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MatematikaRia.com

 This is a Quadratic Equation: (a, b, and c can have any value, except that a can't be 0.)

 The letters a, b and c are the coefficients (you know these) The letter "x" is the variable or unknown (you don't know it yet) (See Basic Algebra Definitions)

 The name Quadratic comes from "quad" meaning square, because the highest exponent is a square (in other words x2).

 In this one a=2, b=5 and c=3 This one is a little more tricky: Where is a? In fact a=1, because we don't usually write "1x2" b=-3 And where is c? Well, c=0, so is not shown. Oops! This one is not a quadratic equation, because it is missing x2 (in other words a=0, and that means it can't be quadratic)

## Why is it special?

Quadratic equations can be solved using a special formula called the Quadratic Formula:

 The "±" means you need to do a plus AND a minus, and so there are normally TWO solutions ! The blue part (b2 - 4ac) is called the discriminant, because it can "discriminate" between the possible types of answer: if it is positive, you will get two solutions if it is zero you get just ONE solution, and if it is negative you get two solutions that include Imaginary Numbers .

## Solving

To solve, just plug the values of a, b and c into the Quadratic Formula, and do the calculations.

### Example: Solve 5x² + 6x + 1 = 0

Quadratic Formula: x = [ -b ± √(b2-4ac) ] / 2a

Coefficients are: a = 5, b = 6, c = 1

Substitute a,b,c: x = [ -6 ± √(62-4×5×1) ] / 2×5

Solve: x = [ -6 ± √(36-20) ]/10 = [ -6 ± √(16) ]/10 = ( -6 ± 4 )/10

Answer: x = -0.2 and -1

(Check:
5×(-0.2)² + 6×(-0.2) + 1 = 5×(0.04) + 6×(-0.2) + 1 = 0.2 -1.2 + 1 = 0
5×(-1)² + 6×(-1) + 1 = 5×(1) + 6×(-1) + 1 = 5 - 6 + 1 = 0)