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Math Help - I need help with polynomial

  1. #1
    dayla
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    I need help with polynomial

    There are two problems that i just am not sure about can someone please help me. It says
    Find tthe follow for f(X)=x^4-8x^2+15
    Approximate all the real zeros to the nearest hundredth



    also i have one more

    find the following for f(X)= x^3+3x^2+9x+27
    A. The number of zeros
    B all zeros exactly
    C. Factor f(X)
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by dayla View Post
    There are two problems that i just am not sure about can someone please help me. It says
    Find tthe follow for f(X)=x^4-8x^2+15
    Approximate all the real zeros to the nearest hundredth

    also i have one more

    find the following for f(X)= x^3+3x^2+9x+27
    A. The number of zeros
    B all zeros exactly
    C. Factor f(X)
    Hello, dayla,

    1) To calculate the zeros use substitution: y = x. Now you have the equation:
    y - 8y + 15 = 0 ==> y = 3 or y = 5

    Re-substitute: x = 3 or x = 5. Thus you get: x1 ≈ -1.732 or x2 ≈ 1.732 or x3 ≈ -2.236 or x4 ≈ 2.236


    With the second problem it is much easier to do C) first:

    f(x) = x + 3x + 9x + 27 = x(x+3) + 9(x+3) = (x+3)(x+9)

    A) A function of third degree has 3 zeros, at least one real zero.

    B) You have to solve:

    0 = x + 3x + 9x + 27 = x(x+3) + 9(x+3) = (x+3)(x+9)

    A product is zero if one (or more) factor(s) are zero:

    x + 3 = 0 ==> x = -3
    x + 9 = 0 ==> x = -9 ==> x = 3i or x = -3i
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