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kerstie

  • 3 years ago

HELP ME PLEASE! Write a polynomial function in standard form with zeros at 5, 2, and 1.

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  1. mathstudent55
    • 3 years ago
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    Think of it this way, instead of solving a polynomial equation and getting x=a, x=b, x=c, you have the answer and you're going backwards. If you had a polynomial equation that factored into (x - 3)(x + 5)(x -2)= 0, the next step would be x -3 = 0 or x + 5 = 0 or x - 2 = 0, and the answer would be x = 3 or x = -5 or x = 2

  2. shahzadjalbani
    • 3 years ago
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    zero means x=0 x=2 or x-2=0 x=5or x-5=0 (x)(x-2)(x-5) The resultant equation is \[x^{3}-7x^{2}+10x\]

  3. mathstudent55
    • 3 years ago
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    Now look at the last line and go backwards. In your problem here, you are given x = 5, x = 2, x = 1 Go 1 step back: x - 5 = 0 or x - 2 = 0 or x - 1 = 0 Go 1 more step back (x - 5)(x - 2)(x - 1) =0 Now multiply these 3 binomials together, collect like terms and write the answer in descending order of the power of x.

  4. kerstie
    • 3 years ago
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    so x^3

  5. mathstudent55
    • 3 years ago
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    Be careful, shahzadjalbani misread the problem and thinks there is a zero at 0. His solution is correct for the problem he solved, but it's not your problem.

  6. mathstudent55
    • 3 years ago
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    Multiply the first two binomials using foil. Then multiply by the third one.

  7. mathstudent55
    • 3 years ago
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    (x - 5)(x - 2)(x - 1) = 0 (x^2 - 2x - 5x + 10)(x - 1) = 0 (x^2 - 7x + 10)(x - 1) = 0 continue...

  8. shahzadjalbani
    • 3 years ago
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    oh sorry x=1 x-1=0 x=2 x-2=0 x=5 x-5=0 Multiply (x-1)(x-5)(x-2) The result would be x^3-8x^{2}+17x-10

  9. kerstie
    • 3 years ago
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    THANKS ALOT

  10. shahzadjalbani
    • 3 years ago
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    Good Luck @kerstie

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