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Section 8e - Quadratic Equations

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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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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

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
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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  • Exercise 8E.2, pg 257

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  • Exercise 8E.3, pg 257

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