Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

Section 8e - Quadratic Equations

ax 2 + bx = 0 Solving Quadratic Equations ax 2 + c = 0ax 2 + bx + c = 0 1) isolate the squared term 2) take the square root of both sides 3) consider  4) solve 1) set equal to zero 2) factor out the GCF 3) use the zero product property 4) solve 1) set equal to zero 2) factor out the GCF, if possible 3) factor 4) use the zero product property 5) solve

Solving Quadratic Equations ax 2 + c = 0 1) isolate the squared term 2) take the square root of both sides 3) consider  4) solve

Solve for x 1) 2x = 152) 2 – 3x 2 = 8

Solve for x 3) (x – 3) 2 = 164) (x + 2) 2 = 11

Zero Product Rule (a.k.a. Null Factor Law)

Solve for x 5) 3x(x – 5) = 0 6) (x – 4)(3x + 7) = 0

ax 2 + bx = 0 Solving Quadratic Equations ax 2 + c = 0 1) isolate the squared term 2) take the square root of both sides 3) consider  4) solve 1) set equal to zero 2) factor out the GCF 3) use the zero product property 4) solve

Solve for x 7) x 2 = 3x8) 2x 2 + 8x = 0

ax 2 + bx = 0 Solving Quadratic Equations ax 2 + c = 0ax 2 + bx + c = 0 1) isolate the squared term 2) take the square root of both sides 3) consider  4) solve 1) set equal to zero 2) factor out the GCF 3) use the zero product property 4) solve 1) set equal to zero 2) factor out the GCF, if possible 3) factor 4) use the zero product property 5) solve

Solve for x 9) x 2 = x ) 3x 2 = 4x – 1

Solve for x 11) 12x 2 – 5x = 2

Homework Exercise 8E.1, pg255 #1acegi #2acei Exercise 8E.2, pg 257 #1acfk Exercise 8E.3, pg 257 #1ace #2acegj #3acegik #4ac #6aceg