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Q: What are roots of the polynomial function F(x)x3-x2-5x-3?
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how many roots does the graphed polynomial function have?

here is the graph


How many unique roots will a third degree polynomial function have?

It can have 1, 2 or 3 unique roots.


what are all of the zeros of this polynomial function f(a)=a^4-81?

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The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.


The rational roots of a polynomial function F(x) can be written in the form where p is a factor of the constant term of the polynomial and q is a factor of the leading coefficient.?

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Can the exponents in a polynomial function be negative?

No. It would not be a polynomial function then.


Is it true that the degree of polynomial function determine the number of real roots?

Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)


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Roots of a polynomial that can be written in the form p over q are called roots?

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A third degree polynomial could have one or three real roots.