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
Jolene says, “See, I just start out by trying to factor. This one can be factored
“But what if it can't be factored?” Raul asked. “What about
“That's easy! I just use the Quadratic Formula,” says Jolene. “And I get… let's see… negative two plus or minus the square root of… two squared… that's 4… minus… eight…”
“Wait!” Raul interrupted. “Right there, see, you don't have to finish.
“Oh, I see,” said Jolene. “I only have to do part of the solution, the part you have to take the square root of.”
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.
For the following, refer to the Math Note above from Lesson 9.2.2 (pg 460 in the student textbook).
; complex roots
Are the roots real or complex?