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4.1 Theorem

If a, b Ï R and ab = 0 then either a = 0 or b = 0

Corollary 1 : If a . b = 0 but a ą 0, then b = 0
Corollary 2 : If a . b . c = 0, a
ą 0, b ą 0, then c = 0
Corollary 3 : If ab = ac, then either a = 0 or b = c

 Example Solution :ExampleSolution : For what values of x is the expression x (3x - 6 ) = 0 ?i.e.     x (3x - 6 ) = 0 Þ either x = 0 or 3x -6 = 0i.e. x = 0 or 3x = 6 x = 2 Therefore, there are two values of x (viz, 0 and 2 ) that make the expression zero. Solve (3x + 1 ) (x + 3) = (x - 2) (x + 3) Transposing ( x + 3 ) ( 3x + 1 ) - ( x - 2 ) ( x + 3 ) = 0 i.e. ( x + 3 ) [ ( 3x + 1 ) - ( x - 2 ) ] = 0 i.e. ( x + 3 ) ( 3x + 1 - x + 2 ) = 0 i.e. ( x + 3 ) ( 2x + 3 ) = 0 i.e. x + 3 = 0 or 2x + 3 = 0 x = -3   or   x = -3/2

Index

4.1 Theorem
4.2 Definition
4.3 Methods of Solving Quadratic Equations

Chapter 5

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