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 :)

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(7193) (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.
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