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Math Help - Sketch graph help

  1. #1
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    Sketch graph help

    The question states:

    Sketch the graphs of y = x^4 & y = 1-3x. Deduce the number of real roots of the equation: x^4+3x-1

    I have sketched both graphics, but I am un-sure as how to prove that the graph has n number of real roots.

    Thank you.
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  2. #2
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    Quote Originally Posted by StephenPoco View Post
    The question states:

    Sketch the graphs of y = x^4 & y = 1-3x. Deduce the number of real roots of the equation: x^4+3x-1

    I have sketched both graphics, but I am un-sure as how to prove that the graph has n number of real roots.

    Thank you.
    The graphs cross where the equations are equal:

    So x^4 = 1 - 3x

    or x^4 + 3x - 1 = 0.


    So what does the number of times the two graphs cross tell you about the number of roots of x^4 + 3x - 1 = 0?
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  3. #3
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    Oh, I see. So when the two graphs "combine" per se, their intersections become the roots? Well in that case there are 2 roots.

    Thanks.
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