## toadytica305 3 years ago List all the real and imaginary zeros of f(x) = x^3+x^2+ 13x - 15... 1 is a zero of the function

1. satellite73

all possible rational roost are number of the form $$\frac{p}{q}$$ where $$p$$ divides the constant ( in your case 15) and $$q$$ divides the leading coefficient, in your case 1

2. satellite73

so the possibilites are $\pm1,\pm3,\pm5,\pm15$

3. satellite73

since you know 1 is a zero, you can factor it as $(x-1)(\text{something})$ and you can find the something by dividing, by synthetic division or by thinking

and to find all real and imaginary zeros

5. satellite73

in this case you get $(x-1) (x^2+2 x+15)$ and the second part you can find the zeros using the quadratic formula they are complex