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).
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.
A quadratic function can have up to two roots. Depending on the discriminant (the expression under the square root in the quadratic formula), it can have two distinct real roots, one repeated real root, or no real roots at all (in which case the roots are complex). Therefore, the total number of roots, considering both real and complex, is always two.
here is the graph
It can have 1, 2 or 3 unique 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.
4, the same as the degree of the polynomial.
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.)
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
Each distinct real root is an x-intercept. So the answer is 4.
Four.Four.Four.Four.
1
5, Using complex numbers you will always get 5 roots.
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).