The expression (6x^{16} - 22 + 6x) is a polynomial in (x) of degree 16. A polynomial of degree (n) can have up to (n) real solutions. Therefore, this polynomial can have up to 16 solutions, depending on the specific values of the coefficients and the nature of the roots.
A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.
No. A polynomial can have as many degrees as you like.
4
As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.
It can have 1, 2 or 3 unique roots.
4, the same as the degree of the polynomial.
Four.Four.Four.Four.
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.)
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.