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Math Help - How would I find this cubic polynomial function?

  1. #1
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    How would I find this cubic polynomial function?

    "Find the cubic polynomial function with two of its zeros 2 and -3+√2 and a y-intercept of 7."
    Answer: y = -0.5(x -2)(x2 + 6x + 7)

    I think that the function will look something similar to: y = k(x-2)(x-(-3+√2))2
    Then I would use the coordinates of the y-intercept (0,7) to find the value of k. However, I'm not sure how to get "(x2 + 6x + 7)".
    Any suggestions would be appreciated, thank you!
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    Re: How would I find this cubic polynomial function?

    Quote Originally Posted by misiaizeska View Post
    "Find the cubic polynomial function with two of its zeros 2 and -3+√2 and a y-intercept of 7."
    Answer: y = -0.5(x -2)(x2 + 6x + 7)

    I think that the function will look something similar to: y = k(x-2)(x-(-3+√2))2
    Then I would use the coordinates of the y-intercept (0,7) to find the value of k. However, I'm not sure how to get "(x2 + 6x + 7)".
    Any suggestions would be appreciated, thank you!
    Hint: If you have a root at x = -3 + \sqrt{2} then you will also have root at x = -3 - \sqrt{2}. At least you will if your polynomial is to have rational coefficients.

    -Dan
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