SOLUTION: f(x) = x^3 + 2x^2 – 5x – 10. Find a bound for the real zeros of f and graph f (x) and find all real zeros of the function. Approximate all irrational zeros rounded to two dec

Algebra ->  Algebra  -> Real-numbers -> SOLUTION: f(x) = x^3 + 2x^2 – 5x – 10. Find a bound for the real zeros of f and graph f (x) and find all real zeros of the function. Approximate all irrational zeros rounded to two dec      Log On

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Question 383381: f(x) = x^3 + 2x^2 – 5x – 10.
Find a bound for the real zeros of f and graph f (x) and find all real zeros of the function. Approximate all irrational zeros rounded to two decimal places.
Answer by Fombitz(13828) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-3%2C3%2C-3%2C3%2C0%2Cx%5E3%2B2x%5E2-5x-10%29
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The real zeros lies between (-3,3).
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graph%28300%2C300%2C-3%2C1%2C-1%2C1%2C0%2Cx%5E3%2B2x%5E2-5x-10%29
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Looks like x=-2 is a zero.
Verify using the equation,
x%5E3%2B2x%5E2-5x-10=%28-2%29%5E3%2B2%28-2%29%5E2-5%28-2%29-10
x%5E3%2B2x%5E2-5x-10=%28-8%29%2B%288%29%2B10-10
x%5E3%2B2x%5E2-5x-10=0
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Since x=-2 is a zero, then x%2B2 is a factor.
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Use polynomial long division to find the other quadratic factor, 

        x^2 - 5
       __________________________
x + 2 | x^3 + 2x^2 - 5x - 10
     - (x^3 + 2x^2)
       ---------------------
                   - 5x - 10
                - (- 5x - 10)
                -------------
                           0

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%28x%5E3+%2B+2x%5E2+-+5x+-+10%29=%28x%2B2%29%28x%5E2-5%29
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For the quadratic equation,
x%5E2-5=0
x%5E2=5
x=0+%2B-+sqrt%285%29
You can approximate those zeros with a calculator to the desired number of decimal places.