Use the Intermediate Value Theorem to show that the polynomial has a zero in the given interval. f(x) = 3x^4 + 4x^3 - 8x - 2; [1, 2] Also, I noticed that there is no x^2 term. Does this change the process in terms of solving the question?
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Originally Posted by magentarita Use the Intermediate Value Theorem to show that the polynomial has a zero in the given interval. f(x) = 3x^4 + 4x^3 - 8x - 2; [1, 2] Also, I noticed that there is no x^2 term. Does this change the process in terms of solving the question? Let . Since f is a polynomial, it is continuous on . We have , so that . So by the intermediate-value theorem there exists in such that . That is, the equation has a solution in the interval .
Originally Posted by masters Let . Since f is a polynomial, it is continuous on . We have , so that . So by the intermediate-value theorem there exists in such that . That is, the equation has a solution in the interval . Thank you very much.
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