Question

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

Answer 1

`(1 +- 6.4i)/7`

Explanation:

`y = 7x^2 - 2x + 6 = 0`
Use the improved quadratic formula, also called the quadratic formula in intercept form (Google, Yahoo, Bing Search).
`D = d^2 = b^2 - 4ac = 4 - 168 = -164` --> `d = +- 12.80( i )`
Since D < 0, there are no real roots. There are 2 complex roots -->
`x = -b/(2a) +- d/(2a) = 2/14 +- (12.80i)/14 = (1 +- 6.4i)/7`