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Using the rational zeros theorem to find all zeros of a polynomial

The function below has at least one rational zero. Use this fact to find all zeros of the function

h(x)=7x^4-9x^3-41x^2+13x+6

if more than one zero, separate with commas. Write exact values, not decimal approximations

  • algebra -

    I tried factors of 6 and found
    f(-2)=0 and f(3) =0

    so after successive synthetic divisions I had the factors,
    (x+2)(x-3)(7x^2 - 2x - 1)

    solving (x+2)(x-3)(7x^2 - 2x - 1) = 0
    x = -2, 3, or (2 ±√32)/14
    = -2, 3, or (1 ± 2√2)/7

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