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**Facts that Matter**

**Quadratic Equations**

An equation of the form ax^{2}+ bx + c = 0, where a, b, c are real numbers, and a â‰ 0, is called a quadratic equation in the variable x.**Examples:**

x^{2}âˆ’ 3x + 4 = 0

2x^{2}âˆ’ 149 = 0**Roots of a Quadratic Equation:**

A value x = Î± is said to be a root of ax^{2}+ bx + c = 0 if it satisfies the equation.**Example:**2 is a root of 3x^{2}âˆ’ x âˆ’ 10 = 0 because 3(2)^{2}âˆ’ 2 âˆ’ 10 = 0.

A quadratic equation has at most two roots (zeroes). Either it has no zero, or two zeroes.

We can solve a quadratic equation by factorisation.**Example:**

Solve 6x^{2}- x - 2 = 0

â‡’ 6x^{2}+ 3x - 4x - 2 = 0

â‡’ 3x(2x + 1) - 2(2x + 1) 0

â‡’ (3x - 2) (2x + 1) = 0

â‡’ 3x - 2 = 0 or 2x + 1 = 0

â‡’ x = 2/3 or x = -1/2

These are the two roots of the equation.

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