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9 November, 13:52

Find b and then solve the equation: 2x^2+bx-10=0, if one of its roots is 5

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  1. 9 November, 16:55
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    Vietas formula tells us that the product of our two roots is equal to the constant term of a quadratic over the leading coefficient, so:

    [tex] r_1r_2=-/frac{-10}{2} / implies 5*r_1=-5 / implies r_1=-1[/tex]

    It also tells us that the b term in our quadratic is equal to the negative of the sum of the terms divided by the leading coefficient, so:

    [tex] r_1+r_2=-/frac{b}{2} / implies 4=-/frac{b}{2} / implies b=-8 [/tex]

    So, one of our roots is 5, the other is - 1, and our b value is 8.
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