Question
Find the complex zeros of the polynomial function. Write f in factored form.
f(x)=3x^4-10x^3-12x^2+122x-39
Please show wrok, I do not understand how to do this.
f(x)=3x^4-10x^3-12x^2+122x-39
Please show wrok, I do not understand how to do this.
Answers
Steve
The 39 and 3 tempt me to try roots like 1,3,1/3. Go for the low-hanging fruit first
use synthetic division to find that
f(-3)=0, so
f(x) = (x+3)(3x^3-19x^2+45x-13)
f(1/3) = 0, so
f(x) = (x+3)(3x-1)(x^2-6x+13)
there are no more real roots
use synthetic division to find that
f(-3)=0, so
f(x) = (x+3)(3x^3-19x^2+45x-13)
f(1/3) = 0, so
f(x) = (x+3)(3x-1)(x^2-6x+13)
there are no more real roots