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Question 907361: For the polynomial f(x) = - x 5 + 3x 3 – x 2 + 7x + 1 state
a. the maximum number of real zeroes that it can have
b. the maximum number of x-intercepts that its graph can have
c. the maximum number of turning points that the graph of the function can have.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! maximum number of real zeroes is 5 because the maximum number of real zeroes is equal to the degree of the equation.
the maximum number of x-intercepts is the same as the maximum number of real zeroes.
the maximum number of turning points is 4 because the maximum number of turning points is always one less than the degree of the equation.
the polynomial can have less than the maximum, but never more.
real roots of a polynomial go down in pairs because, if there are complex roots to the polynomial (not real), they always come in pairs.
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