Question

To find the roots of a polynomial equation you should:

Answer 1

are you really typing

Answer 2

That's the easiest question i have ever answered :D
Ok so,
Here are three important theorems relating to the roots of a polynomial:

(a) A polynomial of n-th degree can be factored into n linear factors.

(b) A polynomial equation of degree n has exactly n roots.

(c) If (x−r) is a factor of a polynomial, then x=r is a root of the associated polynomial equation

Example:
The cubic polynomial f(x) = 4x3 − 3x2 − 25x − 6 has degree 3 (since the highest power of x that appears is 3).

This polynomial can be factored (using Scientific Notebook or similar software) and written as

4x3 − 3x2 − 25x − 6 = (x − 3)(4x + 1)(x + 2)

So we see that a 3rd degree polynomial has 3 roots.

The associated polynomial equation is formed by setting the polynomial equal to zero:

f(x) = 4x3 − 3x2 − 25x − 6 = 0

In factored form, this is:

(x−3)(4x+1)(x+2)=0

We see from the expressions in brackets and using the 3rd theorem from above, that there are 3 roots, x=3, −14, −2.

In this example, all 3 roots of our polynomial equation of degree 3 are real.

Since (x−3) is a factor, then x=3 is a root.

Since (4x+1) is a factor, then x=−14 is a root.

Since (x+2) is a factor, then x=−2 is a root.