Real Zero Bounds for Polynomial Functions

[Loonygirl]

Use the Intermediate Value Theorem and synthetic division to determine whether or not the following polynomials have a real zero between the numbers given.

P(x) = x3 - 3x2 + 2x - 5; Is there a real zero between 2 and 3?

P(x) = x4 + 2x3 + 2x2 - 5x + 3; Is there a real zero between 0 and 1?

P(x) = x3 - 2x2 - 5; Is there a real zero between -1 and -2?

Find the upper and lower bounds for the following polynomials.

P(x) = x3 - x2 + x - 2

P(x) = x3 + 2x2 - 4

 

[HallsofIvy]

That looks very much like homework and I see no attempt on your part to do these problems!

(Odd degree polynomials do NOT have upper and lower bounds on the real numbers.)