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Thread: Quadratic Equation Problems

  1. #1
    Senior Member
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    Quadratic Equation Problems

    1) Solve by factoring:

    $\displaystyle (u+3)/(2u-7)=(2u-1)/(u-3)$

    2) Find the exact solution to:

    $\displaystyle 2(k-1)]=(4-5k)/(k+1)$

    3) Solve this equation:

    $\displaystyle (3t)/(t^2-6)=Sqrt3$
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  2. #2
    Senior Member topher0805's Avatar
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    1) $\displaystyle \frac {u+3}{2u-7} = \frac {2u-1}{u-3}$

    Cross Multiply to get:

    $\displaystyle
    \frac {(u + 3)(u - 3)}{2u - 7} = 2u - 1$

    Multiply both sides by $\displaystyle 2u - 7$:

    $\displaystyle (u + 3)(u - 3) = (2u - 7)(2u - 1)$

    Now multiply out:

    $\displaystyle u^2 + 3u - 3u - 9 = 4u^2 - 2u - 14u + 7$

    Move everything to one side, then simplify:

    $\displaystyle -3u^2 + 16u -16 = 0$

    Now use the quadratic equation to find the roots.

    2) $\displaystyle 2k - 2 = \frac {4 - 5k}{k + 1}$

    Multiply both sides by $\displaystyle k + 1$:

    (2k - 2)(k + 1) = 4 - 5k

    Multiply out:

    $\displaystyle
    2k^2 + 2k - 2k - 2 = 4 - 5k$

    Bring everything to one side, then simplify:

    $\displaystyle 2k^2 + 5k - 6 = 0$

    Now use the quadratic equation.

    3)
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