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27 February, 07:40

List possible rational zeros of f using the rational zero theorem. Then find all thezeros of the function.

f (x) = x^3 + 4x^2 + 9x+36

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  1. 27 February, 07:55
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    The first term is x^3 with coefficient 1. Let's call this p = 1

    The last term is 36, so we'll call this q = 36

    To find all of the possible rational roots or zeros, we divide each factor of q over each factor of p

    Factors of p = 1:

    -1 and 1

    Factors of q = 36:

    -1, 1,

    -2, 2

    -3, 3

    -4, 4

    -6, 6

    -9,9

    -12, 12

    -18,18

    -36,36

    As you can see there's a lot of possible roots. Luckily, p = 1 so that means we simply need to list the factors of q (the plus and minus versions)

    The possible rational roots are listed above when I listed all the possible factors of q. Those are the possible x values that make f (x) equal to 0. You need to plug each of those values into f (x) to see which result in 0. It turns out that only x = - 4 leads to f (x) = 0 being true. None of the other possible rational roots are actual rational roots.
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