Download Solving Equations With Trinomials

Solving Equations Containing Trinomials
• An equation in the form …
x  bx  c  0
2
… can be solved using two methods discussed
previously.
1. Factoring Method
2. Graphing Method
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Review of Factoring Method to Solve Equations
1. Move all non-zero terms to one side of the
equation and simplify.
2. Factor the polynomial expression.
3. Set each factor containing a variable equal to zero.
4. Solve the resulting equations.
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• Example 1:
x  x  12
2
Solve the equation
x  x  12  0
( x  4)( x  3)  0
2
Move all terms to left side
Factor
Set each factor to zero
x40
x3 0
x  4, 3
Solve each equation.
x  3, 4
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Review of Graphing Method to Solve Equations
1. Move all non-zero terms to one side of the
equation and simplify.
2. Put the non-zero expression into y1 on the
calculator and graph.
3. Determine the x-intercepts.
4. The x-values of the x-intercepts are the solutions
to the equation.
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• Example 2:
x  x  12
2
Solve the equation
Move all terms to left side
x  x  12  0
2
y1  x  x  12
2
Put the expression in
for y1 and graph
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5
The x-intercepts are located at
(-3,0) …
… and (4,0)
-5
The solutions are
-10
x  3, 4
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• Example 3:
Solve the equation
 x  8  6 x
Move all terms to right side
since the quadratic term is
positive on that side
0  x  6x  8
2
2
0  ( x  2)( x  4)
Factor
Set each factor to zero
x2 0
x4 0
x  2, 4
Solve each equation.
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Table of Contents