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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. Solving Quadratic Equations. a x 2 + c = 0.

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Section 8e - Quadratic Equations

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Section 8e quadratic equations

Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004


Section 8e quadratic equations

Section 8e - Quadratic Equations


Solving quadratic equations

Solving Quadratic Equations

ax2 + c = 0

isolate the squared term

take the square root of both sides

consider 

solve


Solve for x

Solve for x

1) 2x2+ 1 = 15

  • 2 – 3x2 = 8


Solve for x1

Solve for x

  • (x – 3)2 = 16

  • (x + 2)2 = 11


Zero product rule a k a null factor law

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


Solve for x2

Solve for x

  • 3x(x – 5) = 0

  • (x – 4)(3x + 7) = 0


Solving quadratic equations1

Solving Quadratic Equations

ax2 + c = 0

ax2 + bx = 0

isolate the squared term

take the square root of both sides

consider 

solve

set equal to zero

factor out the GCF

use the zero product property

solve


Solve for x3

Solve for x

  • x2= 3x

  • 2x2+ 8x = 0


Solving quadratic equations2

Solving Quadratic Equations

ax2 + c = 0

ax2 + bx = 0

ax2 + bx + c = 0

set equal to zero

factor out the GCF, if possible

factor

use the zero product property

solve

isolate the squared term

take the square root of both sides

consider 

solve

set equal to zero

factor out the GCF

use the zero product property

solve


Solve for x4

Solve for x

  • x2= x + 30

  • 3x2= 4x – 1


Solve for x5

Solve for x

  • 12x2 – 5x = 2


Homework

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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    #2acegj

    #3acegik

    #4ac

    #6aceg


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