SOLUTION: I am having trouble with learning polynomials. Please help me. Find the complex zeros of the polynomial function. Write f in factored form. f(x)= x^4 + 12x^3 - 9x^2 + 48x - 5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am having trouble with learning polynomials. Please help me. Find the complex zeros of the polynomial function. Write f in factored form. f(x)= x^4 + 12x^3 - 9x^2 + 48x - 5      Log On


   

Question 765788: I am having trouble with learning polynomials. Please help me.
Find the complex zeros of the polynomial function. Write f in factored form.
f(x)= x^4 + 12x^3 - 9x^2 + 48x - 52
The complex zeros of f are: ?
Use the complex zeros to write f in factored form: f(x) = ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+x%5E4+%2B+12x%5E3+-+9x%5E2+%2B+48x+-+52..write -+9x%5E2 as -+13x%5E2%2B4x%5E2
f%28x%29=x%5E4%2B12x%5E3-13x%5E2%2B4x%5E2%2B48x-52....group
f%28x%29=%28x%5E4%2B4x%5E2%29%2B%2812x%5E3%2B48x%29-%2813x%5E2%2B52%29
f%28x%29=x%5E2%28x%5E4%2B4%29%2B12x%28x%5E2%2B4%29-13%28x%5E2%2B4%29
f%28x%29=%28x%5E2%2B12x-13%29+%28x%5E2%2B4%29
f%28x%29=%28x%5E2%2B13x-1x-13%29+%28x%5E2%2B4%29
f%28x%29=%28x-1%29+%28x%2B13%29%28x%5E2%2B4%29
so, to find zeros use zero product rule:
%28x-1%29+%28x%2B13%29%28x%5E2%2B4%29=0
if x-1=0 => x=1
if x%2B13=0 => x=-13
if x%5E2%2B4=0 => x=sqrt%28-4%29=> x=2i or => x=-2i
so, your solutions are:x=1,x=-13 (real),x=2i, and x=-2i (complex)