SOLUTION: My question is: Find the complex zeros of the polynomial function. Write f in factored form f(x)=x^3-8x^2+22x+20 use the complex zeros to write f in factored form thank

Algebra ->  Rational-functions -> SOLUTION: My question is: Find the complex zeros of the polynomial function. Write f in factored form f(x)=x^3-8x^2+22x+20 use the complex zeros to write f in factored form thank       Log On


   

Question 977336: My question is:
Find the complex zeros of the polynomial function. Write f in factored form
f(x)=x^3-8x^2+22x+20
use the complex zeros to write f in factored form

thank you
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) has one real but IRRATIONAL root. The value is very near -0.71. You would have to use some numerical testing to find the value for the accuracy you want. Use the idea that this real (but irrational) root is where f(x) will change signs. Near -0.71, to the left is one sign and to the right is the opposite sign. Keep checking with whatever numeric method you want, for as much accuracy as you require.

When you have your best value for this real, irrational root, then use synthetic division to get the corresponding coefficients of the quadratic factor resulting for the quotient. Solve THAT for ITS complex roots. (General Solution Method for Quadratic Equation).

A graphing tool zoomed in several levels indicates the irrational real root about -0.7097; and you might zoom in further for a better accurate value.