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Thread: value of x coordinate

  1. #1
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    value of x coordinate

    hi, the question i've got is:
    find the exact value of the x coordinate at the point of intersection of-

    the line $\displaystyle 2x + y = 7$ and the curve $\displaystyle y = 4x^2 - 8x - 5$

    the answer is $\displaystyle \frac{1}{4} (3 + \sqrt{57})$ and $\displaystyle \frac{1}{4}(3 - \sqrt{57})$

    could someone show me the steps to arrive at this answer please?
    thanks
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  2. #2
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    Quote Originally Posted by mark View Post
    hi, the question i've got is:
    find the exact value of the x coordinate at the point of intersection of-

    the line $\displaystyle 2x + y = 7$ and the curve $\displaystyle y = 4x^2 - 8x - 5$

    the answer is $\displaystyle \frac{1}{4} (3 + \sqrt{57})$ and $\displaystyle \frac{1}{4}(3 - \sqrt{57})$

    could someone show me the steps to arrive at this answer please?
    thanks
    $\displaystyle y=7-2x$ ---1

    $\displaystyle y = 4x^2 - 8x - 5$ --- 2

    when they intersect , 1=2 .

    $\displaystyle 7-2x=4x^2-8x-5$

    $\displaystyle 4x^2-6x-12=0$

    Use the quadratic formula to solve for x .
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  3. #3
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    yeah thats the problem, i did use the quadratic formula but came up with $\displaystyle 3 \pm \sqrt57$ but i don't understand where the $\displaystyle \frac{1}{4}$ came from?
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  4. #4
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    Quote Originally Posted by mark View Post
    yeah thats the problem, i did use the quadratic formula but came up with $\displaystyle 3 \pm \sqrt57$ but i don't understand where the $\displaystyle \frac{1}{4}$ came from?
    Oh ok ..

    $\displaystyle x=\frac{-(-6)\pm\sqrt{36-4(4)(-12)}}{2(4)}$

    $\displaystyle =\frac{6\pm\sqrt{228}}{8}$

    $\displaystyle =\frac{6\pm2\sqrt{57}}{8}$

    $\displaystyle =\frac{3}{4}\pm\frac{\sqrt{57}}{4}$

    so now what's common ?

    $\displaystyle
    =\frac{1}{4}(3\pm\sqrt{57})
    $
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