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  1. Raul claims that he has a shortcut for deciding what kind of roots a function has. Jolene thinks that a shortcut is not possible. She says you just have to solve the quadratic equation to find out. They are working on y = x2 − 5x − 14.

  2. Use Raul’s method to tell whether each of the following functions has real or complex roots without completely solving the equation. Note: Raul’s method is also summarized in the Math Notes box for this lesson. Homework Help ✎

    1. y = 2x2 + 5x + 4

    2. y = 2x2 + 5x − 3

Calculate the discriminant to see if it is positive or negative.

The discriminant is positive so the roots are real.