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Math Help - f(x) and g(x) compositions

  1. #1
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    f(x) and g(x) compositions

    f(x) = 3x^3 - 2x^2 + x + 7

    g(x) = 2x^2-4

    2 QUESTIONS:


    Find g of f(x)

    AND...


    f(x) has two complex zeros. One is in the 4th quadrant. In what quadrant is the other???
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  2. #2
    Junior Member Ruichan's Avatar
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    g of f(x)
    = 2* (3x^3 - 2x^2 + x + 7)^2 - 4
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  3. #3
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    for the second question i suggest that you use the rational root theorem to find a rational root, lets call it r. we then have

    3x^2-2x^2+x+7=(x-r)Q(x) where Q(x) is a quadratic.

    however if there is not rational root then this becomes quite difficult.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mr_Green View Post
    f(x) has two complex zeros. One is in the 4th quadrant. In what quadrant is the other???
    Two observations:
    The question states there are only two complex zeros.
    f(x) is a cubic polynomial so there can be at most two complex zeros.

    Either way you look at it, there are ONLY two complex zeros of f(x). Since f(x) is a polynomial with real coefficients the two complex zeros are complex conjugates of each other.

    Since one complex zero is in the 4th quadrant, it must have the form a - bi, where a, b > 0. Since the other zero is the complex conjugate of this, the second zero is of the form a + bi, which would be in the first quadrant.

    -Dan
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