Use the rational root theorem.shorty888 said:A. List possible rational Zeros
If x = 2 is a root, then the polynomial is divisible by x - 2 by the polynomial remainder theorem. You can use polynomial long division to find the ratio, which is a quadratic polynomial. Its roots can be found using the quadratic formula.shorty888 said:B. find all the zeros (real and complex) of the function (test x=2 as a rational zero using the synthetic division?
A polynomial function is a type of mathematical function that is made up of variables, coefficients, and exponents. It takes the form of f(x) = anxn + an-1xn-1 + ... + a1x + a0, where an to a0 are constants and x is the variable.
To find the zeros of a polynomial function, you need to set the function equal to zero and solve for the variable. This will give you the x-values where the function intersects the x-axis, also known as the zeros or roots of the function.
Real zeros are values that make the polynomial function equal to zero when plugged in for the variable, resulting in a real number. Complex zeros, on the other hand, involve the imaginary unit i and can result in complex numbers. A polynomial function can have both real and complex zeros.
A polynomial function will have complex zeros if it has complex coefficients, meaning some of the constants in the function are complex numbers. Additionally, the polynomial function may have complex zeros if the degree of the function is odd.
Yes, you can graph a polynomial function with complex zeros. The x-intercepts of the graph will represent the real and complex zeros of the function. However, because complex numbers cannot be plotted on a traditional x-y graph, the complex zeros will appear as points on the y-axis.