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Method of completing the square : This method works with both real and imaginary roots.

1) Express ax^{2} + bx + c = 0 as ax^{2} + bx = - c

2) Make sure that a = 1 (if a ¹ 1, multiply both sides by 1/a )

3) To make L. H. S. a perfect square we add ( 1/2 ´ coefficient of x )^{2}

i.e. (b/2)^{2}

4) Find the square roots of both sides.

5) Solve the resulting equation.

Example Solve x^{2} - 4x + 1 = 0

Solution : x^{2} - 4x + 1 = 0

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Index

4.1 Theorem 4.2 Definition 4.3 Methods of Solving Quadratic Equations

Chapter 5