Material Taken From:

Mathematicsfor 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

Solving Quadratic Equations

ax2 + c = 0

1)isolate the squared term

2)take the square root of both sides

3)consider 4)solve

Solve for x

1) 2x2 + 1 = 15 2) 2 – 3x2 = 8

Solve for x

3) (x – 3)2 = 16 4) (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

ax2 + bx = 0

Solving Quadratic Equations

ax2 + c = 0

1)isolate the squared term

2)take the square root of both sides

3)consider 4)solve

1)set equal to zero2)factor out the

GCF3)use the zero

product property4)solve

Solve for x7) x2 = 3x 8) 2x2 + 8x = 0

ax2 + bx = 0

Solving Quadratic Equations

ax2 + c = 0 ax2 + bx + c = 0

1)isolate the squared term

2)take the square root of both sides

3)consider 4)solve

1)set equal to zero2)factor out the

GCF3)use the zero

product property4)solve

1)set equal to zero2)factor out the

GCF, if possible3)factor4)use the zero

product property5)solve

Solve for x

9) x2 = x + 30 10) 3x2 = 4x – 1

Solve for x

11) 12x2 – 5x = 2

Homework

• Exercise 8E.1, pg255

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#2acei• Exercise 8E.2, pg 257

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• Exercise 8E.3, pg 257

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