find all roots of the polynomial equation. x^5+3x^4-2x^3-14x^2-15x-5=0.

Trying x = ± 1, ± 5

I get a zero when x = -1
by synthetic division:
(x+1)(x^4 + 2x^3 - 4x^2 - 10x - 5) = 0
well, what do you know, x = -1 works again, so
(x+1)(x+1)(x^3 + x^2 - 5x - 5) = 0
grouping the last part
(x+1)(x+1)( x^2(x+1) - 5(x+1) ) = 0
(x+1)(x+1)(x+1)(x^2 - 5) = 0

(x+1)^3 (x^2 - 5) = 0
x = -1 or x = ± √5

that's exactly what I got but it keeps saying it is wrong.

To find all the roots of the polynomial equation, x^5 + 3x^4 - 2x^3 - 14x^2 - 15x - 5 = 0, we can use the numerical methods for finding roots such as the Newton-Raphson method or the bisection method. However, these methods can be time-consuming and require manual calculations. Alternatively, we can use a mathematical software or calculator capable of solving equations directly.

Here's how you can use a mathematical software like MATLAB or Wolfram Alpha to find the roots:

1. MATLAB:
- Open MATLAB or any similar software.
- Define the polynomial equation: f(x) = x^5 + 3x^4 - 2x^3 - 14x^2 - 15x - 5.
- Use the "roots" function to find all the roots of the polynomial equation.
- The MATLAB code will be:
```matlab
syms x
f(x) = x^5 + 3*x^4 - 2*x^3 - 14*x^2 - 15*x - 5;
roots = solve(f(x) == 0, x);
disp(roots);
```
- Execute the code, and MATLAB will output all the roots of the polynomial equation.

2. Wolfram Alpha:
- Go to the Wolfram Alpha website (www.wolframalpha.com) or use the Wolfram Alpha app.
- Enter the polynomial equation: x^5 + 3x^4 - 2x^3 - 14x^2 - 15x - 5 = 0.
- Press Enter or click the "Submit" button.
- Wolfram Alpha will compute and display all the roots of the polynomial equation in the results section.

Using these methods, you can find the roots of the given polynomial equation quickly and accurately.