19 01 Solving Quadratic Equations in Factored Form

19. 01 Solving Quadratic Equations in Factored Form

Recall that when solving an equation the variable must be isolated on one side. To do this, remove any numbers from that side by undoing the operations. Solve: 3 x – 7 = 11 +7 + 7 3 x = ___ 18 ___ 3 3 x = 6

A Quadratic Equation is an equation where the largest power of x is 2. Examples: x 2 + 7 x + 12 = 0 x 2 – 4 = 0 3 x 2 – 17 x + 20 = 0 The Standard Form of a Quadratic Equation ax 2 + bx + c = 0 where a > 1 and ( a , b , c ) are integers.

The Zero – Product Property If a · b = 0 , then a = 0 or b = 0 If the product of two expressions equal zero, then one of the two expressions must equal zero. To solve a quadratic equation already in factored form, set each factor equal to 0 and solve the equations.

If a · b = 0 , then a = 0 or b = 0 Solve: ( x + 3 )( x – 6 ) = 0 x+3 = 0 – 3 x = – 3 or . Solve: x– 6 = 0 +6 +6 x = 6. 8 x( x + 1 ) = 0 8 x =___ 0 ___ 8 8 x = 0 or x+1 = 0 – 1 x = – 1. Set both factors equal to 0 Solve both equations.

If a · b = 0 , then a = 0 or b = 0 Solve: ( 2 x + 4 )( 3 x – 2 ) = 0 2 x + 4 – 4 2 x = ___. 2 = 0 or – 4 ____ 2 x = – 2 3 x – 2 = 0 +2 +2 3 x = ___ 2 ___. 3 3 2 __ x = 3 Set both factors equal to 0 Solve both equations.

Try This: If a · b = 0 , then a Solve: 4 x( x – 3 ) = 0 4 x = ___ 0 or x– 3 = 0 ___ +3 +3 4 4 x = 3 x = 0. Solve: (3 x – 6 )( x + 5 ) = 0 3 x – 6 = 0 or x + 5 = 0 +6 +6 – 5 3 x = ___ 6 ___ x =– 5 3 3 x = 2. . = 0 or b = 0 Set both factors equal to 0 Solve both equations.