How do you find the zeros, real and imaginary, of y=-4x^2+4x-16 using the quadratic formula?

1 Answer
Nghi N.
Aug 6, 2016

2 imaginary roots:
x = (1 +- isqrt15)/2

Explanation:

Use the improved quadratic formula in graphic form (Socratic Search)
y = -4x^2 + 4x - 16 = 0
D = d^2 = b^2 - 4ac = 16 - 256 = -240 < 0.
Since D < 0, there are no real roots. There are 2 imaginary roots.
D = 240i^2= (16)(15)i^2 --> d = +- 4isqrt15
x = -b/(2a) +- d/(2a) = -4/-8 +- 4isqrt15/8 = (1 +- isqrt15)/2

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