SOLUTION: How to prove there is at least one real zero of the equation P(x)= -3x^3+x^2-4x+8 just looking for p(?)=0 Thanks :)

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: How to prove there is at least one real zero of the equation P(x)= -3x^3+x^2-4x+8 just looking for p(?)=0 Thanks :)      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 603619: How to prove there is at least one real zero of the equation
P(x)= -3x^3+x^2-4x+8
just looking for p(?)=0
Thanks :)
Answer by richard1234(5390) About Me  (Show Source):
You can put this solution on YOUR website!
Polynomial is of odd degree, this means that P(x) approaches infinity as x approaches infinity; P(x) approaches negative infinity as x approaches negative infinity.

Also, we know that P(x) is continuous everywhere. Therefore by the intermediate value theorem, P(x) has at least one real zero.