Question

How do you find the roots, real and imaginary, of `y=-23x^2+5x+2` using the quadratic formula?

Answer 1

`(5 +- sqrt209)/46`

Explanation:

Use the improved quadratic formula (Socratic Search)
`y = -23x^2 + 5x + 2 = 0`
`D = d^2 = b^2 - 4ac = 25 + 184 = 209` --> `d = +- sqrt209`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = -5/-46 +- sqrt209/-46 =`
`= (5 +- sqrt209)/46`