Quadratic Equation

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)

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

Examples of Quadratic Equations:

		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)

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:

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

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)

Some equations may not look like quadratic equations, but with a little clever work they can be made into one:

In disguise	What to do	In standard form	a, b and c
x² = 3x -1	Move all terms to left hand side	x² - 3x + 1 = 0	a=1, b=-3, c=1
2(x² - 2x) = 5	Expand (undo the brackets), and move 5 to left	2x² - 4x - 5 = 0	a=2, b=-4, c=-5
x(x-1) = 3	Expand, and move 3 to left	x² - x - 3 = 0	a=1, b=-1, c=-3
5 + 1/x - 1/x² = 0	Multiply by x²	5x² + x - 1 = 0	a=5, b=1, c=-1