A cubic polynomial can have three zeros because its highest power (or degree) is three. A quadratic polynomial may have no real solution but a cubic polynomial always has at least one real solution. If a cubic polynomial does have three zeros, two or even all three of them may be repeated.
A cubic polynomial will have 3 zeroes since its highest power (or degree) is 3.
Similarly, a cubic polynomial can have a maximum of three zeroes.
The degree of the function indicates how many zeros the given function will have, therefore, the cubic function, since the degree is three, can have at most three zeros and it is not possible to have more than three.
A cubic function can also have two local extreme values (1 max and 1 min), as in the case of f(x) = x3 + x2 + x + 1, which has a local maximum at x = −1 and a local minimum at x = 1/3. These are the only options.
Therefore, a cubic polynomial can have a minimum of one and a maximum of three zeroes.
Just as a quadratic equation may have two real roots, so a cubic equation has possibly three. But unlike a quadratic equation which may have no real solution, a cubic equation always has at least one real root.
A cubic polynomial will have 3 zeroes since its highest power (or degree) is 3.
What is Zeros of a Cubic Polynomial? Zeros of a cubic polynomial is the point at which the polynomial becomes zero. A cubic polynomial can have three zeros because its highest power (or degree) is three. A quadratic polynomial may have no real solution but a cubic polynomial always has at least one real solution.
The answer is no. Just as a quadratic polynomial does not always have real zeroes, a cubic polynomial may also not have all its zeroes as real. But there is a crucial difference. A cubic polynomial will always have at least one real zero.
Any nonconstant polynomial p(x,y)∈C[x,y] will always have infinitely many zeros. If the polynomial is only a function of x, we may pick any value for y and find a solution (since C is algebraically closed).
A cubic Equation has degree 3, so the maximum number of roots will be 3.
Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order. For example, a cubic function can have as many as three zeros, but no more. This is known as the fundamental theorem of algebra.
We can have cubic polynomials having less than 3 zeroes. For example, The polynomial y = x3 + x2 + x + 1 has a degree of 3 but has only one real root, that is, x = -1.
A cubic function has the standard form of f(x) = ax3 + bx2 + cx + d. The "basic" cubic function is f(x) = x3. You can see it in the graph below. In a cubic function, the highest power over the x variable(s) is 3.
Sample Answer: A cubic function can have 1, 2, or 3 distinct and real roots.
A polynomial of degree four is said to be the fourth-degree polynomial. It can have at most four distinct zeroes.
So a polynomial of degree 4 have 4 zeroes. Hence, the maximum number of zeroes that a polynomial of degree 4 can have is 4.
Hence, more than 3 polynomials can have the zeroes - 2 and 5 .
A cubic function with real coefficients has either one or three real roots (which may not be distinct); all odd-degree polynomials with real coefficients have at least one real root.
The polynomial x^4 + 4x^2 + 5 has four real zeroes.
Therefore the numbers of roots of a cubic equation are three and these roots can be real roots or the complex roots. We know that any real root can also be written in the complex form i.e. with the imaginary part \[a + \left( 0 \right)i\]. Therefore, we can say that a cubic equation can have three complex roots.
Are all cubic equations solvable? If so, are all polynomials solvable? If by “solvable” you mean “can find a zero value” — that is, an x-intercept — then yes, all cubic equations have at least one real solution.
A polynomial of degree n can have at most n zeros.