Find roots 'a' and 'b' of the quadratic equation 2(x^2) + 6x + 7 = 0

We know to find roots of any quadratic equation we use the quadratic formula, [-b +- (b^2 - 4ac)^(1/2)]/2a where a=2, b=6, and c=7.

Plug these values in and we obtain, [-6 +- (-20)^(1/2)]/4. [Remember for imaginary numbers, (-a)^(1/2) = (a^(1/2))*((-1)^(1/2)) = a^(1/2) *i.]

So we have, [-6 +- 25^(1/2)i]/4 since 20^(1/2) = (45)^(1/2) = 25^(1/2). Therefore, our two roots are

a = (-3/2) + [5^(1/2)/2]*i b = (-3/2) - [5^(1/2)/2]*i