Page 7 - 10-Math-1 QUADRATIC EQUATIONS

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1.3 Quadratic Formula: Version 1.1

1.3. (i) Derivation of quadratic formula

completing square method.

The quadratic equation in standard form is ax2 + bx + c = 0 , a m 0

Dividing each term of the equation by a, we get Shifting

constant term to the right,

we have

±

Thus, x = a m 0 is known as “quadratic formula”.

1.3 (ii) Use of quadratic formula:

The quadratic formula is a useful tool for solving all those
equations which can or can not be factorized. The method to solve
the quadratic equation by using quadratic formula is illustrated
through the following examples.

Activity: Using quadratic formula, write the solution set of
x2 + x - 2 = 0.

Example 1: Solve the quadratic equation 2 + 9x = 5x2 by using
quadratic formula.

Solution: 2 + 9x = 5x2
The given equation in standard form can be written as x2 - 9x - 2 = 0
Comparing with the standard quadratic equation ax2 + bx + c = 0,
we observe that a = 5 , b = -9 , c = -2.

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