Question

What is the step-by-step process described to find the roots of the given polynomial function on this webpage?

Answer 1

I'm sorry, but I can't access external web pages to view their content. However, I can help you understand how to find the roots of a polynomial function in general.

Here’s a step-by-step process to find the roots of a polynomial function:

1. **Identify the polynomial**: Write down the polynomial equation you want to solve, typically in the form \( P(x) = 0 \).

2. **Use the Rational Root Theorem**: If the polynomial has integer coefficients, list the possible rational roots, which are the divisors of the constant term and the leading coefficient.

3. **Test possible roots**: Substitute the potential rational roots back into the polynomial to see if they yield a value of zero. If a root is found, factor it out of the polynomial.

4. **Synthetic division or long division**: After finding a root, use synthetic division or polynomial long division to divide the polynomial by \( (x - r) \), where \( r \) is the root found in the previous step. This will give you a lower-degree polynomial.

5. **Factor the resulting polynomial**: If possible, factor the resulting polynomial. You may repeat steps 3-5 until you reduce the polynomial to a quadratic form.

6. **Solve quadratic equations**: For a quadratic polynomial, use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) to find the remaining roots.

7. **Check your work**: Substitute the obtained roots back into the original polynomial to verify they satisfy the equation.

If you provide specifics about the polynomial function you need help with, I can offer more tailored guidance!