query20

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course Mth163

July 11,2013 2:39pm

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If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

020. `query 20

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Question: `qWhat are the zeros of f(x) = 2x - 6 and g(x) = x + 2?

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Your solution:

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x=3,x=-2

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confidence rating #$&*: 3

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Given Solution:

`a** f(x) = 2x - 6 is zero when 2x - 6 = 0. This equation is easily solved to yield x = 3.

g(x) = x + 2 is zero when x + 2 = 0. This equation is easily solved to yield x = -2. **

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Self-critique (if necessary):

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Self-critique rating:OK

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Question: `qWhat does the quadratic formula give you for the zeros of the quadratic polynomial q(x)?

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Your solution:

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2x^2 -2x -12

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This is what you get when you expand the polynomial.

To see the point of this question you have to apply the quadratic formula to the equation

2 x^2 - 2 x - 12 = 0.
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confidence rating #$&*:

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Given Solution:

`a** We get q(x) = f(x) * g(x) = (2x - 6) ( x + 2) = 2x ( x + 2) - 6 ( x + 2) = 2 x^2 + 4 x - 6 x - 12 = 2 x^2 - 2 x - 12.

This polynomial is zero, by the quadratic formula, when and only when

x = [ -(-2) +- sqrt( (-2)^2 - 4(2)(-12) ] / (2 * 2) = [ 2 +- sqrt( 100) ] / 4 = [ 2 +- 10 ] / 4.

Simplifying we get x = (2+10) / 4 = 3 or x = (2 - 10) / 4 = -2.

This agrees with the fact that f(x) = 0 when and only when x = -3, and g(x) = 0 when and only when x = 2.