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## SS2: MATHEMATICS - 2ND TERM

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Lesson 5, Topic 2
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# Solving Quadratic Equations by the Formulae

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#### Topic Content:

• Solving Quadratic Equations by the Formulae

The method of completing the square can be best used to establish a formula for the solution of the quadratic equation of the form

$$\scriptsize ax^2 \: +\: bx\: +\: c = 0$$

The formula is given as:

x = $$\large \frac{-b \pm \sqrt {b^2 \: – \: 4ac}}{2a}$$

The formula above is known as the quadratic formula, where

a is the coefficient of $$\scriptsize x^2$$

b = coefficient of x

c = constant term.

Note that, the quadratic formula is particularly used to solve quadratic equations, which cannot be solved using factorization method.

### Example 5.2.1:

i. $$\scriptsize 3x^2 \: – \: 5x \: – \: 9 = 0$$

ii. $$\scriptsize – 3x^2 = (x\:+\:2)(x\:-\:1)$$

iii. $$\scriptsize \left(\scriptsize 2x \:- \: 3 \right)^2 = x^2$$

iv. $$\scriptsize -4x^2 \: + \: 2x \: + \: 6 = 0$$

Solution:

i. $$\scriptsize 3x^2 \: – \: 5x \: – \: 9 = 0$$

Let a = 3, b = -5 and c = -9

Using the factor formula we have:

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