Four.
Four.
Four.
Four.
A third degree polynomial is called a cubic - regardless of how many terms it has, it is named after the highest power.x3+ x - 1 is still a cubic, despite the lack of an x2term. Likewise, x2- 4 is still a quadratic, and x4- 2x is called a quartic.
Given any set of 6 numbers it is easy to find a rule based on a polynomial of order 5 such that the polynomial generates those numbers. There are infinitely many polynomials of orders 6, 7, 8 etc and also non-polynomial answers.One possible answer, out of these infinite possibilities isUn = (4n5 - 37n4 + 663 + 2415n2 - 730n + 456)/24 for n = 1, 2, 3, ...
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y = x2-4x+4 Since the highest degree term is 2, it must have 2 roots
both are roots both grow under ground both hold the plant firmly
It can have 1, 2 or 3 unique roots.
4, the same as the degree of the polynomial.
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
5, Using complex numbers you will always get 5 roots.
According to the rational root theorem, which of the following are possible roots of the polynomial function below?F(x) = 8x3 - 3x2 + 5x+ 15
A third degree polynomial could have one or three real roots.
here is the graph
1
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.)
To find the roots of the polynomial (3x^5 + 2x^3 + 3x), we can factor out the common term, which is (x): [ x(3x^4 + 2x^2 + 3) = 0. ] This shows that (x = 0) is one root. The quartic polynomial (3x^4 + 2x^2 + 3) does not have real roots (as its discriminant is negative), meaning it contributes no additional real roots. Therefore, the polynomial has only one real root, which is (x = 0).
None, it involves the square root of a negative number so the roots are imaginary.
Upto 4. If the coefficients are all real, then it can have only 0, 2 or 4 real roots.