How do you use the discriminant to determine the numbers of solutions of the quadratic equation #z^2 + z + 1 = 0# and whether the solutions are real or complex?

1 Answer
Jul 8, 2018

Answer:

no real solutions

Explanation:

Given: #z^2 + z + 1 = 0#

When the equation is in the form: #Az^2 + Bz + C = 0# the discriminant is #B^2 - 4AC#

When #B^2 - 4AC = 0# there is 1 real solution

When #B^2 - 4AC >0# and not a perfect square: 2 real solutions

When #B^2 - 4AC < 0# there are no solutions, the answers are imaginary.

For the given equation:

#B^2 - 4AC = 1-4(1)(1) = 1-4 = -3 => #no real solutions