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

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.