A
The general form of a polynomial equation of degree 4 is $ A{x^4} + B{x^3} + C{x^2} + Dx + E = P(x) $ . Some names are assigned to the polynomials of different degrees based on the degree of that polynomial.
A polynomial function that has four real roots is a fourth-degree polynomial.
x4 - 2x3 + 6x2 + 8x - 40 = 0 is your 4th order polynomial in standard form that has the above zeros.
A fourth-degree polynomial means that the highest exponent out of all the variables present in the polynomial is 4. We can call a polynomial a trinomial if it has three terms. Therefore, a fourth-degree trinomial with three terms and the highest exponent out of all the variables is 4.
The Fundamental Theorem of Algebra states that the degree of a polynomial is the maximum number of roots the polynomial has. A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots.
A polynomial of degree four is said to be the fourth-degree polynomial. It can have at most four distinct zeroes.
(c) 9x4 - x3 - x/5 is the polynomial of degree 4 as maximum power is given as 4 and it also satisfies the definition of the polynomial.
Quartic Function: A quartic function is a function with a degree of 4, meaning that the highest exponent of the function is 4. The standard form of a quartic function is f ( x ) = a 0 x 4 + a 1 x 3 + a 2 x 2 + a 3 x + a 4 .
A polynomial with four terms is sometimes called a quadrinomial. However, it is rarely used. While a polynomial with 1, 2 and 3 terms is called monomial, binomial and trinomial, respectively, a polynomial with more than 3 terms does not have a special name.
Degree 5 – quintic. Degree 6 – sextic (or, less commonly, hexic)
The graph of a fourth-degree polynomial will often look roughly like an M or a W, depending on whether the highest order term is positive or negative. If the coefficient of the leading term, a, is positive, the function will go to infinity at both sides.
A polynomial containing five terms is called quintrinomial polynomial. y 6 + 8 y 5 + 9 y 4 + 9 y 2 + 7.
Fourth-degree polynomials are also known as quartic polynomials. Quartics have these characteristics: Zero to four roots. One, two, or three extrema.
In other words, a quintic function is defined by a polynomial of degree five. Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum.
In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph.