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Math Help - How do I find the sum and product of the roots of this equation?

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    How do I find the sum and product of the roots of this equation?

    How do I find the sum and product of the roots of this equation?


    The equation is 7x^2-4x+2=0.
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    Quote Originally Posted by deathtolife04 View Post
    How do I find the sum and product of the roots of this equation?


    The equation is 7x^2-4x+2=0.
    Well, the direct way is to solve the equation and find the sum and the product!

    To show how to do this without actually solving:
    x_{\pm} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    So
    x_{+} + x_{-} = \frac{-b + \sqrt{b^2 - 4ac}}{2a} + \frac{-b - \sqrt{b^2 - 4ac}}{2a} = \frac{-b}{2a} + \frac{-b}{2a} = -\frac{b}{a}

    and
    x_{+} \cdot x_{-} = \left ( \frac{-b + \sqrt{b^2 - 4ac}}{2a} \right ) \left ( \frac{-b - \sqrt{b^2 - 4ac}}{2a} \right )

    Recall that (p + q)(p - q) = p^2 - q^2, so
    x_{+} \cdot x_{-} = \left ( \frac{-b}{2a} \right ) ^2 - \left ( \frac{\sqrt{b^2 - 4ac}}{2a} \right ) ^2

    x_{+} \cdot x_{-} = \frac{b^2}{4a^2} - \frac{b^2 - 4ac}{4a^2} = \frac{c}{a}

    -Dan
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    Quote Originally Posted by deathtolife04 View Post
    How do I find the sum and product of the roots of this equation?

    The equation is 7x^2-4x+2=0.
    Hello,

    you can use the theorem of Vieta(?) (that's the name I know for this theorem)

    if you have a quadratic equation:

    ax^2+bx+c=0~\Longrightarrow~x^2+\frac{b}{a}x+\frac  {c}{a}=0 with the solutions x_1 \text{ and } x_2 then the theorem says:

    x_1 \cdot x_2 = \frac{c}{a} and

    x_1 + x_2 = -\frac{b}{a}
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