### Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem 9-90

9-90.

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 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

For the following, refer to the Math Note above from Lesson 9.2.2 (pg 460 in the student textbook).

*b*^{2} − 4*ac* = −7; complex roots

*b*^{2} − 4*ac* = 49

Are the roots real or complex?