Question 675111: HOW DO I FIND the zeros for a polynomial x^3-6x^2+9 I need some guidance please explain and show the steps Thank you Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! Usually you find the zeros of a polynomial by factoring it. The zeros of the polynomial will be the set of all x values that make one of the factors zero.
In the case of a quadratic polynomial, you also have the Quadratic Formula that can be used. (There is also formulas for cubic equations, like the one in this equation, but they are complex and are not often taught.)
Your equation is not quadratic and it does not factor. So to find the zeros there are three possibilities:
The equation you posted had an error. Please correct the equation and, if you can't figure out how to factor it then post a question about the correct equation.
Use the cubic formulas (which is the only way you will find exact expressions for the zeros). If your teacher meant for you to use these, they should have been taught to you. (They are so complex I can never remember them myself.)
Use your graphing calculator to graph the equation (Below you will see the graph. Notice how the graph crosses the x-axis three times. The x-coordinate of each of these x-intercepts is a zero of your polynomial. Since the polynomial doesn't factor these zeros are all irrational.) Now use the trace function to find these x-coordinates. (Since the zeros are irrational, the best you can do is get a decimal approximation for the zeros.)
(