SOLUTION: If the discriminant of a complete quadratic equation is 8, what is the nature of its root? A. Imaginary and identical B. Imaginary and Unequal C. Real and identical D. Real and

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Since the discriminant is greater than 0, this means that the equation will have 2 distinct real roots. So the answer is D) Real and unequal

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Let be the discriminant, i.e. .

If , then the roots are a conjugate pair of complex numbers of the form .

If , the roots are real and equal. (Also described as a single root with a multiplicity of 2)

If , the roots are real and unequal.

Note that choice A is never possible, and choice B only occurs when in equals 0 so that the complex roots become .