What are the roots of 2x^2+4x+7? Use the quadratic formula. Show your work

Question

What are the roots of 2x^2+4x+7? Use the quadratic formula. Show your work

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Claire 2 weeks 2022-01-08T19:54:23+00:00 1 Answer 0 views 0

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    2022-01-08T19:55:46+00:00

    Answer:

    The roots are

    x=-1+i\frac{\sqrt{10}}{2}

    x=-1-i\frac{\sqrt{10}}{2}

    Step-by-step explanation:

    we have

    2x^2+4x+7

    To find the roots equate the equation to zero

    so

    2x^2+4x+7=0

    we know that

    The formula to solve a quadratic equation of the form

    ax^{2} +bx+c=0

    is equal to

    x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

    in this problem we have

    2x^2+4x+7=0

    so

    a=2\\b=4\\c=7

    substitute in the formula

    x=\frac{-4\pm\sqrt{4^{2}-4(2)(7)}} {2(2)}

    x=\frac{-4\pm\sqrt{-40}} {4}

    Remember that

    i=\sqrt{-1}

    so

    x=\frac{-4\pmi\sqrt{40}} {4}

    x=\frac{-4\pm2i\sqrt{10}} {4}

    simplify

    x=\frac{-2\pm i\sqrt{10}} {2}

    therefore

    The roots are

    x=\frac{-2+i\sqrt{10}} {2}=-1+i\frac{\sqrt{10}}{2}

    x=\frac{-2-i\sqrt{10}} {2}=-1-i\frac{\sqrt{10}}{2}

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