SOLUTION: please help. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = 8x^3

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Question 616968: please help.
Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]
-------
f(-1) = 8*-1 - 10*1 + 3*-1 + 5
f(-1) = -8 -10 -3 + 5 < 0
------
f(0) = 5
---
Since f(-1) is negative
And f(0) is positive
and
Since f is continuous on [-1,5] there must be a zero on that interval.
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cheers,
Stan H.
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Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

If

where, presuming real function values:

$\sgn(x) = \begin{cases}<BR> -1 & \text{if } x < 0, \\<BR> 0 & \text{if } x = 0, \\<BR> 1 & \text{if } x > 0. \end{cases}$

then has a real zero on []

John

My calculator said it, I believe it, that settles it

SOLUTION: please help. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]