Question

How do you find the roots, real and imaginary, of `y=2x^2 -42x-28` using the quadratic formula?

Answer 1

`x = (21 +- sqrt497)/2`

Explanation:

`f(x) = 2x^2 - 42x - 28 = 0`
`f(x) = 2(x^2 - 21x - 14) = 0`
Use the improved quadratic formula in graphic form:
`D = d^2 = b^2 - 4ac = 441 + 56 = 497` --> `d = +- sqrt497`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = 21/2 +- sqrt497/2 = (21 +- sqrt497)/2`