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Thread: Finding the real solutions

  1. #1
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    Finding the real solutions

    Hi

    Can someone help me how to solve the following:

    1) Find the real solutions of the cubic equation:$\displaystyle 9x^3 + 8x +6$

    This is what i have done:

    $\displaystyle let x = x $

    $\displaystyle 9x^2 +8+6 = 0$

    $\displaystyle 9x^2 = -14$

    $\displaystyle x^2=\frac{-14}{9}$

    $\displaystyle x=1.2472$

    2) Find the inequality corresponding to the graph:


    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi

    Can someone help me how to solve the following:

    1) Find the real solutions of the cubic equation:$\displaystyle 9x^3 + 8x +6$

    This is what i have done:

    $\displaystyle let x = x $ , what do u mean ?

    $\displaystyle 9x^2 +8+6 = 0$ , how did the x^3 become x^2

    $\displaystyle 9x^2 = -14$

    $\displaystyle x^2=\frac{-14}{9}$ , you can't have negative values in the square root

    $\displaystyle x=1.2472$ , this is wrong


    hi

    this can't be solved algebraically (Perhaps it can , but i don see how). The fastest way to solve it is by using a calculator OR you can also approximate the roots using the newton-raphson method .
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  3. #3
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    Quote Originally Posted by mathaddict View Post

    hi

    this can't be solved algebraically (Perhaps it can , but i don see how). The fastest way to solve it is by using a calculator OR you can also approximate the roots using the newton-raphson method .

    ok thanks,

    also the second question forgot to add that there were 4 answers to choose from:

    $\displaystyle y>0.272x+0.428-\frac{2}{x}$

    $\displaystyle y>-0.419x-0.360$

    $\displaystyle y>-1.291x-1.45$

    $\displaystyle y>-0.521x+0.603-\frac{1}{x}$

    $\displaystyle y>1.97x-0.142-\frac{1}{x^2}$
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  4. #4
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    It should be obvious that the lower boundary of that region is a straight line and so its equation is linear. That excludes all except the second and third. In the picture it looks like when x= 0, y is between -.25 and -.50. Which of the given options is that?
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