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college algebra--need help please!!

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use the intermediate value theorem to show that the polynomial function has a zero in the given interval.

f(x)=x^5-x^4+9x^3-5x^2-16x+5;[1.3,1.6]

f(x)1.3= ? simplify answer
f(x)1.6= ? "

  • college algebra--need help please!! -

    1.3^5 = 3.71293----> 3.71
    1.3^4 = 2.8561 ---->-2.86
    1.3^3 = 2.197 ----->19.77
    1.3^2 = 1.69------->-8.45
    -16*1.3 ----------->-20.8
    +5 ----------------> +5
    add
    f(1.3) = -3.63
    now do f(1.6)
    1.6^5 = 10.48576 ----> 10.5
    1.6^4 = 6.5536 ------>-6.55
    1.6^3 = 4.096 -------> 36.9
    1.6^2 = 2.56 -------->-12.8
    1.6*-16 ------------->-25.6
    +5------------------->+5
    add
    f(1.6) = 7.45
    ah ha!
    somewhere in between there this function which is continuous crossed the x axis at least once to get from -3.63 to + 7.45
    Therefore it had at least one zero in there.

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