### Home > CCA2 > Chapter 8 > Lesson 8.2.2 > Problem 8-88

8-88.

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*=*x*^{2}− 5*x*− 14.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 ✎

*y*= 2*x*^{2}+ 5*x*+ 4*y*= 2*x*^{2}+ 5*x*− 3

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

The discriminant is positive so the roots are real.