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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.)
Is it possible to find a polynomial of degree 3 that has -2 as its only real zero?
5
Is the square root of x a polynomial?
No,
How many x-intercepts does a quartic polynomial function having 4 distinct real roots have?
Each distinct real root is an x-intercept. So the answer is 4.
What set of numbers does pi belong to?
Real, complex, quaternion, etc. But more specifically it's a transcendental real number, not being the root of an integer polynomial (and certainly not the ratio of two integers).
