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Math Help - Write a Function For This Polynomial

  1. #1
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    Write a Function For This Polynomial

    Draw the graph and write a function for the polynomial that fits the following description.

    p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

    P(X)= _____________________




    Can someone please help me with this problem? I'd really appreciate it. Thank you in advance.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DesiKid89 View Post
    Draw the graph and write a function for the polynomial that fits the following description.

    p is a fourth-degree polynomial with x-intercepts -2, -1, and 5 and y-intercept -50; p(x) is positive only on the interval (-2 , -1 ).

    P(X)= _____________________




    Can someone please help me with this problem? I'd really appreciate it. Thank you in advance.
    try drawing axis with the intervals given. by marking the intervals where the graph is positive and/or negative (with say a tick for positive and an x for negative) you would realize that the zero x = 5 is a double root.

    thus we have: P(x) = (x + 2)(x + 1)(x - 5)^2

    now expand
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  3. #3
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    Ok, I expanded it out and I ended up with:

    P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

    ....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DesiKid89 View Post
    Ok, I expanded it out and I ended up with:

    P(X)= x^4 - 7x^3 - 5x^2 - 55x + 50

    ....and apparently that ended up being wrong, so can someone explain what I did wrong (and possibly what the correct answer may be)?
    it should be a +55x here. but there is something else wrong. we need a negative x^4 graph to fulfill the conditions. so multiply through by -1 (after you fix the sign on the 55x)

    so in short, you must find P(x) = -(x + 2)(x + 1)(x - 5)^2
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  5. #5
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    Yeah now I got:

    P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

    ...and that was right, thanks a lot man. Your like my new math idol, lol.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DesiKid89 View Post
    Yeah now I got:

    P(X)= -x^4 + 7x^3 + 3x^2 -55x -50

    ...and that was right, thanks a lot man. Your like my new math idol, lol.
    you're welcome... you had a math idol??
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