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Math Help - Roots of equation?

  1. #1
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    Roots of equation?

    Find the value of p and the roots of the equation 2xsquared - 33x + p = 0
    given that one root is ten times the other root.
    I dont how to start this question, can someone help me please.
    Thanks!
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Detanon View Post
    Find the value of p and the roots of the equation 2xsquared - 33x + p = 0
    given that one root is ten times the other root.
    I dont how to start this question, can someone help me please.
    Thanks!
    You can use the caret symbol ^ to signify "to the power of". This sign also works in LaTeX

    2x^2 - 33x+p=0

    Use the quadratic formula

    x = \frac{33\pm \sqrt{1089-8p}}{4}

    Split the \pm sign to see the two roots more clearly.

    For the fun of it I will choose the positive root to be bigger than the negative root although either should work

    x_1 = \frac{33+\sqrt{1089-8p}}{4}

    x_2 = \frac{33-\sqrt{1089-8p}}{4}

    x_1=10x_2 \: \rightarrow \: \: \frac{33+\sqrt{1089-8p}}{4} = 10 \cdot \frac{33-\sqrt{1089-8p}}{4}

    Solve for p (and the denominator will cancel immediatly)
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  3. #3
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    How do you solve for p..?
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  4. #4
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    Quote Originally Posted by Detanon View Post
    How do you solve for p..?
    Multiply the final equation by 4. Then solve 33 + \sqrt{a} = 10 (33 - \sqrt{a}) for a where a = 1089 - 8p. Then use the value of a to solve for p.
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