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.
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.
If there is one variable. Then put each variable equal to zero and then solve for the other variable.
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
Solve the equation - by whatever means available to you: factorising, graphical, numerical approximations, etc.
when the equation is equal to zero. . .:)
by synthetic division and quadratic equation
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.
Polynomial fuction in standard form with the given zeros
If there is one variable. Then put each variable equal to zero and then solve for the other variable.
A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.
Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.
A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0. For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.
The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.
3y2-5xyz yay i figured it out!!!!
Solve the equation - by whatever means available to you: factorising, graphical, numerical approximations, etc.
The polynomial is (x + 1)*(x + 1)*(x - 1) = x3 + x2 - x - 1