The discriminant of a quadratic equation is -5. Which answer describes the number and type of solutions of the equation: 1 complex solution 2 real solutions 2 complex solutions 1 real solution?

1 Answer
Andy Y.
May 24, 2017

Your quadratic equation has #2# complex solutions.

Explanation:

The discriminant of a quadratic equation can only give us information about an equation of the form:

#y=ax^2+bx+c# or a parabola.

Because the highest degree of this polynomial is 2, it must have no more than 2 solutions.

The discriminant is simply the stuff underneath the square root symbol (#+-sqrt(" ")#), but not the square root symbol itself.

#+-sqrt(b^2-4ac)#

If the discriminant, #b^2-4ac#, is less than zero (i.e., any negative number), then you would have a negative under a square root symbol. Negative values under square roots are complex solutions. The #+-# symbol indicates that there is both a #+# solution and a #-# solution.

Therefore, your quadratic equation must have #2# complex solutions.

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