^{n}+ bx

^{n-1}+ cx

^{n-3}+ ….......+z = 0, where a, b, c..... Are constants and are not equals to 0, than this equation is known as a polynomial equation. Polynomial equations are divided into two parts -

For finding roots of polynomial, we use following steps -

Step 1: First of all, we convert our high order polynomial equation into Quadratic Equation by using the division method, like we have a high order polynomial equation,

x

^{3}+ px

^{2}+ qx + r = 0, then we substitute ‘x’ as a (y – p/3),

It gives a simple polynomial equation y

^{3}+ ay + b = 0,

Then we convert this equation into quadratic equation-

(y – v) . (y

^{2}+ ay + b) = 0,

Step 2: After evaluation of a quadratic equation, we get one root (y – v) and other root is calculated by following roots of this quadratic equation (y

^{2}+ ay + b),

y = [-a +/- √(a

^{2}– 4b)]/2,

This gives two roots of ‘y’.

So, finally we get 3 roots of this cubic polynomial equation.

Now we take an example to understand the process of finding roots of polynomial:

Example: Find the roots of following polynomial equation -

x

^{4}– 2x

^{2}– 3x – 2 = 0?

Solution: We use following steps for evaluating the roots of given polynomial equation -

Step 1: First of all we convert equation into quadratic equation,

x

^{4}– 2x

^{2}– 3x – 2 = 0,

=> (x + 1)(x - 2)(x

^{2}+ x + 1) = 0,

Step 2: Now we calculate roots of quadratic equation -

x

^{2}+ x + 1 = 0,

x = -1/2 ± √3/2i,

So, finally we get following roots of polynomial -

(x + 1) (x – 2) and x = -1/2 ± √3/2i.