SOLUTION: Answer the following questions for the function f(x)=x^8-3x^5+22 What is the maximum number of zeros that the function can have? What is the maximum number of x intercepts that

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Question 142437: Answer the following questions for the function f(x)=x^8-3x^5+22
What is the maximum number of zeros that the function can have?
What is the maximum number of x intercepts that the function can have?
What is the maximum number of turning points that the function can have?
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Answer by solver91311(12126) (Show Source):
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Since the function is degree 8, it has exactly 8 zeros. It has a maximum of 8 real zeros. The function will have an x-intercept corresponding to every real zero, so it has a maximum of 8 x-intercepts. A polynomial function of degree n has at most n - 1 turning points, so 8 - 1 = 7 turning points, maximum.