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Math Help - no integral zero

  1. #1
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    no integral zero

    rove that x^3+4x +7 has no integral zeros
    its x grade question(age 13 -14)without using calculus
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  2. #2
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    Do you mean "no integer zeroes"?
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by ayushdadhwal View Post
    rove that x^3+4x +7 has no integral zeros
    its x grade question(age 13 -14)without using calculus
    Using the rational roots theorem

    Rational root theorem - Wikipedia, the free encyclopedia

    The only possible rational and hence possible integral zero are

     \pm 1 \pm 7

    and since none of these are zero's we are done
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  4. #4
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    Hello, ayushdadhwal!

    \text{Prove that }\,x^3+4x +7\,\text{has no integral zeros. }

    \text{It's x grade question (age 13 -14) without using calculus.}

    \text{Let }\,y \:=\:x^3+4x+7\,\text{ and plot some points on its graph.}

    . . \begin{array}{c||c|c|c|c|c|} x & \text{-}3 & \text{-}2 & \text{-}1 & 0 & 1 \\ \hline  y & \text{-}32 & \text{-}9 & 2 & 7 & 12 \end{array}

    We find that the graph is strictly increasing
    . . and the only x-intercept occurs between (-2, -9) and (-1, 2)
    . . (when the graph crosses the x-axis).


    Hence, the only zero of the function occurs between x = \text{-}1 and x = \text{-}2.

    Therefore, there are no integral zeros.

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