The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
You could try setting the function equal to zero, and finding all the solutions of the equation. Just a suggestion.
The answer can be any number that you like: it is always possible to find a polynomial of order 5 to fit the given numbers and any other number.The lowest degree polynomial that will fit the given numbers is the quadraticUn = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives the next number as -57.The answer can be any number that you like: it is always possible to find a polynomial of order 5 to fit the given numbers and any other number.The lowest degree polynomial that will fit the given numbers is the quadraticUn = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives the next number as -57.The answer can be any number that you like: it is always possible to find a polynomial of order 5 to fit the given numbers and any other number.The lowest degree polynomial that will fit the given numbers is the quadraticUn = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives the next number as -57.The answer can be any number that you like: it is always possible to find a polynomial of order 5 to fit the given numbers and any other number.The lowest degree polynomial that will fit the given numbers is the quadraticUn = (9n2 - 205n + 792)/2 for n = 1, 2, 3, .. . and that gives the next number as -57.
4x2 + 3x - 6 is a second degree polynomial. Since the polynomial function f(x) = 4x2 + 3x - 6 has 2 zeros, it has 2 linear factors. Since we cannot factor the given polynomial, let's find the two roots of the equation 4x2 + 3x - 6 = 0, which are the zeros of the function. 4x2 + 3x - 6 = 0 x2 + (3/4)x = 6/4 x2 + (3/4)x + (3/8)2 = 6/4 + 9/64 (x + 3/8)2 = 105/64 x + 3/8 = ± √(105/64) x = (-3 ± √105)/8 x = -(3 - √105)/8 or x = -(3 + √105)/8 Thus, the linear factorization of f(x) = 4[x + (3 - √105)/8][x + (3 + √105)/8].
There are only three roots given so, in general, there is no unique answer. However, if it is a real polynomial, then its complex roots must come in conjugate pairs. Then 6i is a root implies that -6i is a root. So the polynomial is (x - 4)(x + 3)(x + 6i)(x - 6i) = (x2 - x - 12)(x2 + 36) = x4 + 36x2 - x3 - 36x - 12x2 - 432 = x4 - x3 + 24x2 - 36x - 432
when the equation is equal to zero. . .:)
Find All Possible Roots/Zeros Using the Rational Roots Test f(x)=x^4-81 ... If a polynomial function has integer coefficients, then every rational zero will ...
If the cubic polynomial you are given does not have an obvious factorization, then you must use synthetic division. I'm sure wikipedia can tell you all about that.
The remainder theorem states that if you divide a polynomial function by one of it's linier factors it's degree will be decreased by one. This theorem is often used to find the imaginary zeros of polynomial functions by reducing them to quadratics at which point they can be solved by using the quadratic formula.
If there is one variable. Then put each variable equal to zero and then solve for the other variable.
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
To find the number of real zeros of a function, you can use the Intermediate Value Theorem and graphing techniques to approximate the number of times the function crosses the x-axis. Additionally, you can apply Descartes' Rule of Signs or the Rational Root Theorem to analyze the possible real zeros based on the coefficients of the polynomial function.
Multiply x3 - 2x2 - 13x - 10
The zeros of a quadratic function, if they exist, are the values of the variable at which the graph crosses the horizontal axis.
Do mean find the polynomial given its roots ? If so the answer is (x -r1)(x-r2)...(x-rn) where r1,r2,.. rn is the given list roots.
If the discriminant is positive, then the function has two real zeros. If it is zero, then the function has one real zero. If it is negative, then it has two complex conjugate zeros.This assumes that we are talking about a standard second order polynomial equation, i.e. quadratic equation, in the form Ax2 + Bx + C = 0, and that the discriminant is B2 - 4AC, which is a part of the standard solution of these kind of equations.
If you have the zeros of a polynomial, it is easy, almost trivial, to find an expression with those zeros. I am not sure I understood the question correctly, but let's assume you have the zero 2 with multiplicity 2, and other zeros at 3 and 5. Just write the expression: (x-2)(x-2)(x-3)(x-5). (Example with a negative zero: if there is a zero at "-5", the factor becomes (x- -5) = (x + 5).) You can multiply this out to get the polynomial if you like. For example, if you multiply every term in the first factor with every term in the second factor, you get x2 -2x -2x + 4 = x2 -4x + 4. Next, multiply each term of this polynomial with each term of the next factor, etc.