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?

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Answer 1 · 2018-07-08T06:34:42

no real solutions

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