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

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