A polynomial can be expressed in terms that have only positive integer exponents and mathematical operations of addition, subtraction and multiplication.

A polynomial equation is an equation that can be written in the form

axn + b x n - 1 + c xn - 2 + ........ + rx + s = 0

where a, b, ….,r are the coefficients and s is a constant.

We call the largest exponent of x as the degree of the polynomial.

A polynomial equation is a polynomial which is set equal to zero in an equation.

Example:  5x - 2 = 0

        x2 - 4x + 8 = 0

        x4 + 5x2 - 1 = 0.

Polynomial Equation Solver is a mathematical tool which will solve all the polynomial equations.
In general, the number of solutions equals the degree of the polynomial. A linear equation has a unique solution, a quadratic equation has two solutions (or one solution with multiplicity of 2) etc.

We use 4 steps to solve a polynomial equation in one variable. The following example uses all four steps but some equations may not require all of them.

Example: Solve 15x2 + 8x = 0

Solution:

Step 1: solve the equation 15x2 + 8x = 0

          $ \Rightarrow $   x ( 15 x + 8 ) = 0

Step 2 : Use  zero multiplicity property

Step 3 : x = 0 or 15x + 8 = 0

So the solution is ( 0, $\frac{-8}{15}$)

Solving Polynomial Equations


Solving a quadratic equation by using quadratic formula. There are various ways of solving a quadratic polynomial like factorization or completing a square but these methods are not always viable to work .The quadratic formula can be applied to any quadratic equation.

The solution to general quadratic equation ax2 + bx + c = 0
                         
                      x = $\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

The quantity $ \bigtriangleup $ = $ \sqrt{b^{2}-4ac} $ is called as the discriminant of the quadratic.

If $ \bigtriangleup $ is positive,  then there are two distinct real zeros (solutions ).

If $ \bigtriangleup $ = 0 ,then there is only one real solution $\frac{-b}{2a}$

If $ \bigtriangleup $ < 0 , then the solutions are not real.

Solving Cubic equation by finding one factor 

Start with the equation ax3 + bx2 + cx + d = 0

By trial and error method find one solution x = s . the possible value for 

s = $ \pm$ $ \frac{factors\ of\ c}{factors\ of\ a} $

Once the first factor x - s is found ,then by using long division /synthetic division other factors are obtained.