Question

How do you find the roots, real and imaginary, of `y=7x^2+4x + 6` using the quadratic formula?

Answer 1

`(-2 +- isqrt38)/7`

Explanation:

Use the improved quadratic formula (Google, Yahoo Search)
y = 7x^2 + 4x + 6 = 0
D = d^2 = b^2 - 4ac = 16 - 168 = - 152
Since D < 0, there are no real roots. There are 2 complex roots.
`d^2 = 152i^2` --> `d = +- 2isqrt38`
`x = -b/(2a) +- d/(2a) = -4/14 +- (2isqrt38)/14 = (-2 +- isqrt38)/7`