Question

How to find the roots of a polynomial equation of any degree?

Answer 1

The most versatile way of finding roots is factoring your polynomial as much as possible, and then setting each term equal to zero. This makes a lot more sense once you've followed through a few examples. Consider the simple polynomial x2 – 4_x:_

Factor the Polynomial

A brief examination shows that you can factor x out of both terms of the polynomial, which gives you:

x(x – 4)

Answer 2

Answer:

Answer:

Here one root is x = 1 so (x - 1) is a factor. i.e

{x}^{3} - {x}^{2} - 3 {x}^{2} + 3x + 2x - 2 =x

3

−x

2

−3x

2

+3x+2x−2=

{x}^{2} (x - 1) - 3x(x - 1) + 2(x - 1) =x

2

(x−1)−3x(x−1)+2(x−1)=

(x - 1)( {x}^{2} - 3x + 2) =(x−1)(x

2

−3x+2)=

(x - 1)( {x}^{2} - 2x - x + 2) =(x−1)(x

2

−2x−x+2)=

(x - 1)(x(x - 2) - 1(x - 2)) =(x−1)(x(x−2)−1(x−2))=

(x - 1)(x - 2)(x - 1) = (x - 1) {}^{2} (x - 2)(x−1)(x−2)(x−1)=(x−1)

2

(x−2)