Question 1042946: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]
a. no real roots; f(x) = (x2 + 1)(3x2 + 1)
b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)
c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)
d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)
Answer by ikleyn(52780)   (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]
a. no real roots; f(x) = (x2 + 1)(3x2 + 1)
b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)
c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)
d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)
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They ask you to apply the intermediate value theorem.
Do you know what "the intermediate value theorem" is?
I specially copied and pasted this citation for you from this Wikipedia article.
In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, [a, b],
as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b)
at some point within the interval.
This has an important corollary: If a continuous function has values of opposite sign inside an interval, then it has a root
in that interval (Bolzano's theorem).
It seems strange to me what follows after the assignment.
In n.n. a, b, c, and d I see the listing of the roots and factoring formulas,
and I do not understand how it correlates with the assignment.
Let me say more.
No one factorization a), b), c), d) corresponds to the given polynomial.
My impression is that somebody, who understands NOTHING in these topics, mistakenly merged different parts of different assignments in one post.
And then sent it trice !!!
DIAGNOSIS. This post is one big fatal error and does not deserve any serious consideration.
The sender must ask pardon for sending this post.
Ask the pardon three times, according to the number of issued copies of this post.
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