Intermediate Value Theorem and Boundedness?

Question

please explain me how to do these

1.)

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

2.)

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

please dont just give me the answer

i ACTUALLY want to learn how to do these

please explain and thank you

Answer 1

1. p(2) = -5

p(3) = 1

since 0 is between -5 & 1, then there is a value x such that p(x) = 0.

intermediate value theorem says , that if you change signs from one end of the interval to the other, you must cross zero.. . .

2. P(0) = 3 .. . .. . P(1) = 3

then we cannot say anything using the intermediate value theorem.