SOLUTION: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval f(x)=-2x^4+2x^2+4; [-2,-1]

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Question 935701: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval f(x)=-2x^4+2x^2+4; [-2,-1]
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The square parentheses mean you can INCLUDE the boundaries of the interval.

x=-2:
-2%28x%5E4-x%5E2-2%29
-2%28%28-2%29%5E4-%28-2%29%5E2-2%29
-2%2816-4-2%29
%28neg%29%28pos%29
NEGATIVE

x=-1:
-2%28%28-1%29%5E4-%28-1%29%5E2-2%29
-2%281-1-2%29
-2%28-2%29
neg%2Aneg
POSITIVE

Polynomial functions are continuous everywhere. The function changes signs inside the given interval, so f must cross the x-axis, and therefore has a zero in the interval.