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DeadShot

  • one year ago

Which of the following is a polynomial with roots - square root of 5, square root of 5, and -3 ? x3 - 2x2 - 3x + 6, x3 + 2x2 - 3x - 6, x3 - 3x2 - 5x + 15, or x3 + 3x2 - 5x - 15?

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  1. tcarroll010
    • one year ago
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    If you have roots of: a, b, and c your polynomial has the form: (x - a)(x - b)(x - c) = 0 Substitute a, b, and c for the given roots and multiply the expression out on the left side.

  2. DeadShot
    • one year ago
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    x^3 -2.25x^2+2.25x^2-3x2-2.25x+2.25x-3x-15

  3. DeadShot
    • one year ago
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    simplified, it's x^3-3x^2-3x-15, right?

  4. tcarroll010
    • one year ago
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    You wouldn't even have to ask that last question because you have 4 choices and this choice is not even listed among them. Here's a hint on how to expand that expression I gave you: (x - a)(x - b)(x - c) = 0 [(x - a)(x - b)](x - c) = 0 [x^2 - (a + b)x + ab](x - c) = 0 [x^2 - (a + b)x + ab]x - [x^2 - (a + b)x + ab]c = 0

  5. DeadShot
    • one year ago
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    [x^2-(-2.25+2.25)x + (-2.25)*2.25]x-[x^2-(-2.25+2.25)x + (-2.25)*2.25]-3=0

  6. tcarroll010
    • one year ago
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    Where are you getting +-2.25 from? Neither has anything to do with sqrt(5).

  7. DeadShot
    • one year ago
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    sqrt(5) is approx 2.25

  8. tcarroll010
    • one year ago
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    You don't want to be working with approximations here.

  9. DeadShot
    • one year ago
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    ok

  10. DeadShot
    • one year ago
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    x^3 - 3x^2 - 5x + 15

  11. tcarroll010
    • one year ago
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    I would suggest evaluating the following first: [x - sqrt(5)][x + sqrt(5)] That correspond to the leftmost factors. Get that down to a trinomial.

  12. DeadShot
    • one year ago
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    that would be x^2-5

  13. DeadShot
    • one year ago
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    (x^2-5) (x-3)=x^3 - 3x^2 - 5x + 15

  14. DeadShot
    • one year ago
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    right?

  15. tcarroll010
    • one year ago
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    The third root is "-3", so you have: [x - (-3)] or (x + 3) for that third factor. I think that's where you having your trouble. When you subtract a negative, it's like adding a positive.

  16. tcarroll010
    • one year ago
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    So, taking up from where you were writing: (x^2 - 5)(x + 3) = 0 And then expand that. You are very close to your answer now.

  17. DeadShot
    • one year ago
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    so, it's x^3+3x^2-5x-15?

  18. tcarroll010
    • one year ago
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    Yes! Excellent! Just remember about subtracting negatives and you will be ok.

  19. DeadShot
    • one year ago
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    Okay, Thanks for the help!

  20. tcarroll010
    • one year ago
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    You're welcome! Good luck to you in all of your studies and thx for the recognition! @DeadShot

  21. DeadShot
    • one year ago
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    No problem!

  22. malice
    • 8 days ago
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    x3 + 3x2 - 5x - 15 is not the correct answer (just took the test)

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