A polynomial function f, is a function of the form f(x) = anxn + an-1xn-1 + ... + a2x2 + a1x1 + a0 where a0, a1...an are real numbers. It will soon become more understandable with some more examples. If "n" is not zero, then f is said to have degree n. A polynomial f(x) with real coefficients and of degree n has n zeros (not necessarily all different). Some or all are real zeros and appear as x-intercepts when f(x) is graphed. To make it more simple lets start by explaining the word polynomial, it is the word which comes made of two terms "poly" states many and nominal states "terms". Nomenclature of different polynomial functions, depending upon the terms present in the equation is done such as, if it has only one term it is called as monomial, if two terms it is called as binomial and if three terms it is called as trinomial, and so on with increasing variable terms.
Lets make it more elaborate with the help of examples, X + X>2 = 4 is an example of monomial, x + y = 5 is an example of binomial, X + Y + Z = 7 is an example of trinomial. When there are equations involving polynomial it is known as a Polynomial equation. For solution of a polynomial equation different values for variables in the equation satisfying the equation along with the given constant coefficient values used in the polynomial.
Lets see it practically with the help of some example, 5 x + 6 y = 0 is a polynomial equation, for a point A in a plane having coordinates (0, 0). Co-ordinates states value of x = 0, and y = 0 for this equation. Substituting values of x and y in the Polynomial equations we have 5 (0) + 6 (0) = 0 + 0 = 0. As the values on both sides of the equation are equal this is a solution of the equation. Hence point A is the solution for this Polynomial equations.
Can you help me with some of my math homework and show me how to do it? I just don't get some of it.. :/
ReplyDelete1) List all the possible roots of the function: f(x) = 2x^4 + 4x^3 + 7x^2 - 6x +12.
2) Find the roots of each polynomial equation:
A. x^3 - x^2 - 10x - 8 =0
B. x^3 - x^2 + 9x = 0
3) Find two additional roots of 1 - 4i and 3 + 2i.
4) Find a third degree polynomial equation with rational coefficients that has roots of 5 and 4i.
5) Find the number of complex roots, the possible number of real roots, and the possible rational roots of x^7 - 2x^6 + 3x^2 - 2x + 5.
Umm you don't have to help me with all of these, but these are just the problems i don't understand this problem of polynomial equation. I have a test tomorrow! D: