Posted by **Alley** on Sunday, March 31, 2013 at 7:28pm.

Use the intermediate theorem to show that the polynomial function value has a zero in the given interval

f(x)=x^5-x^4+8x^3-7x^2-17x+7; [1.6,1.8]

Find the value of f(1.6)

Find the value of f(1.8)

- Algebra -
**Reiny**, Sunday, March 31, 2013 at 8:31pm
My calculator gave me a negative value for f(1.6)

and a positive value for f(1.8)

I wonder how the graph got from below the x-axis to above the x-axis in that little interval.

- Algebra -
**Alley**, Sunday, March 31, 2013 at 8:42pm
What does that mean?

- Algebra -
**Reiny**, Sunday, March 31, 2013 at 8:50pm
mmmhh?

I plugged in x = 1.6 and got some negative value

I plugged in x = 1.8 and got some positive value

so we have two points of your graph

one is (1.6, -?) , the other is (1.8, + ?)

so one is below the x-axis , the other is above the x-axis

make a rough sketch of this situation, (it doesn't make any difference how far down or how far up you place points)

join your two points.

I see them **crossing or intersecting **the x-axis.

Don't we call the place where a graph cuts the x-axis, "the zero of the function" ??

I see such a point between x = 1.6 and 1.8

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