Use the intermediate value theorem to show that the polynomial fx)x 2x-9 has a r

Question

Use the intermediate value theorem to show that the polynomial fx)x 2x-9 has a real zero on the interval [1,3]. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The polynomial has a real zero on the given interval, because f(-x) has variation(s) in sign. O B. The polynomial has a real zero on the given interval, because1) and f(3)-are both negative. O C. The polynomial has a real zero on the given interval, because f(1)-and f(3)-are opposite in sign 0 D. The polynomial has a real zero on the given interval, because f(1)-1 and f(3), are both positive O E. The polynomial has a real zero on the given interval, because f(1)-and f(3)-are outside of the interval O F. The polynomial has a real zero on the given interval, because (1)and f(3)-are complex conjugates.

Explanation / Answer

f (x)=x3+2x-9

Using intermediate value theorem

on [1,3] we have

f (1)=1+2-9

=-6

and

f (3)=(3)3+2×3-9

=27+6-9

=24

Answer (C)

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