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.
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 = 2x2 + 5x + 4
y = 2x2 + 5x − 3
Calculate the discriminant to see if it is positive or negative.
The discriminant is positive so the roots are real.