Page 4 - 10-Math-1 QUADRATIC EQUATIONS

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Version 1.1 Example 1: Solve the quadratic equation 3x2 - 6x = x + 20 by

factorization.

Solution: 3x2 - 6x = x + 20 (i)

The standard form of (i) is 3x2 - 7x - 20 = 0 (ii)

Here a = 2 , b = - 7 , c = - 20 and ac = 3 x -20 = -60

As -12 + 5 = - 7 and -12 x 5 = - 60, so

the equation (ii) can be written as

3x2 - 12x + 5x - 20 = 0

3x ( x - 4 ) + 5 ( x - 4) = 0

or 3x ( x - 4 ) + 5 ( x - 4 ) = 0

⇒ (x - 4) (3x + 5) = 0

Either x - 4 = 0 or 3x + 5 = 0 , that is, x = 4 or 3x = -5 ⇒ x = -

∴ x = - , 4 are the solutions of the given equation.

Thus, the solution set is

Example 2: Solve 5x2 = 30x by factorization.

Solution: 5x2 = 30x
5x2 - 30x = 0 which is factorized as
5x(x - 6) = 0
Remember that: Cancelling of x on both sides of 5x2 = 30x means
the loss of one root i.e., x = 0
Either 5x = 0 or x - 6 = 0 ⇒ x = 0 or x = 6
⇒ x = 0, 6 are the roots of the given equation.
Thus, the solution set is {0, 6}.

1.2(ii) Solution by completing square:

To solve a quadratic equation by the method of completing square
is illustrated through the following examples.

Example 1: Solve the equation x2 - 3x - 4 = 0 by completing square.

Solution: x2 - 3x - 4 = 0 (i) Shifting constant term -4 to the right, we

have x2 - 3x = 4.

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