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

Question 149765: Use the Intermediate Value Theorem to determine if has a zero in the interval [1,2]
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To use the intermediate value theorem, simply evaluate the endpoints of the interval.

Let's evaluate the left endpoint

Start with the given equation.

Plug in .

Raise to the 5th power to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the function value at is . This makes the point (1,-4) which tells us that the y-coordinate is negative.

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Now let's evaluate the right endpoint

Start with the given equation.

Plug in .

Raise to the 5th power to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the function value at is . This makes the point (2,51) which tells us that the y-coordinate is positive.

Since the sign of the y-coordinate transitioned from negative to positive on the interval [1,2], this means that the graph must have crossed the x-axis somewhere in the interval. So there is a zero in the interval [1,2].

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