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Math Help - Verify that each function has given roots

  1. #1
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    Verify that each function has given roots

    Graph each of the following functions. Verify that each function has the given equal roots.

    f(x)= 3x - 4x; two roots that equal 0

    I have graphed it, but what else am I supposed to do?
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  2. #2
    Senior Member Sambit's Avatar
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    you have provided only a function which can not have a root. i suppose you wanted to say the roots of the equation  3x^3 - 4x^2 = 0. in that case, the graph will be like this:-http://www4d.wolframalpha.com/Calcul...20&w=300&h=187
    clearly, you get the solutions from x^2 (3 x-4) = 0 ,ie,  x=0, x=0 and  3x-4=0,ie, x=4/3
    thus, the equation has 3 roots, 2 of which are 0, and the third one is \frac{4}{3}
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  3. #3
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    Since you have the graph you should observe that the graph is tangent to the x-axis at x= 0 while it crosses the x-axis at 4/3. The fact that the graph touches or crosses the x-axis tells you that the equation has a root (and the function has a "zero") at that point. The fact that the graph is tangent to the x-axis there tells you that it has a double (or higher) root.
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