Using the examples as models, try solving these quadratic equations using the quadratic formula or taking square roots and your understanding of complex number solutions:

Why didn't the equation x² − 2x − 3 = 0 have imaginary or complex solutions?

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Since the number “c” is negative 3, the discriminant (the number under the radical) is positive, and therefore the solutions are real. Or the trinomial can be factored to (x + 1)(x − 3) = 0, which yields the solutions -1 and 3, both real and rational.

What is the distinctive characteristic of a complex number on the graph of one of these equations?

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The graph would never cross the x-axis.