SOLUTION: Use the Intermediate Value Theorem to determine if P(x) = 2x^5

SOLUTION: Use the Intermediate Value Theorem to determine if P(x) = 2x^5 - 7x +1 has a zero in the intervals [1,2].

Question 90245: Use the Intermediate Value Theorem to determine if P(x) = 2x^5 - 7x +1 has a zero in the intervals [1,2].
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's evaluate

Start with the given polynomial

Plug in

Raise 1 to the fifth power to get 1

Multiply 2 by 1 to get 2

Multiply 7 by 1 to get 7

Now combine like terms

Now let's evaluate

Start with the given polynomial

Plug in

Raise 2 to the fifth power to get 32

Multiply 2 by 32 to get 64

Multiply 7 by 2 to get 14

Now combine like terms

Since our y-value changes from a negative value to a positive value in the interval [1,2] this means there is a zero in this interval.
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