How To Solve Quadratic Equation

How To Solve Quadratic Equation

How To Solve Quadratic Equation

Quadratic Equations are very important in mathematics and physics. In practice we often model physical systems into mathematical models which results in different types of equations including quadratic equation. Solving the quadratic equation means finding the roots of it. A general quadratic equation can be written as

ax^2 + bx + c = 0

In which a,b and c are constants and x is an unknown called a variable whose value has to be found. Those values of x that satisfy above equation when substituted with x are called roots of the equation.
For a quadratic equation there are always two roots because the maximum power of x in the equation is 2.

Note: By satisfying the equation means that the left hand side should be equal to the right hand side.

The roots of quadratic equation can be classified in three types namely

Real and Distinct
  The real means that the root is a constant integer or fraction while the distinct means that both of the roots are different. For example 2 and 3

Imaginary and Distinct
  These type of roots are distinct but are complex numbers i.e. a+bi form. for example  2+3i and 0+2i

Repeated Roots

Some times it also happens that upon solving, both of the roots are same they can be either be real or complex. These roots are called repeated roots or roots of multiplicity 2. foe example 1 and 1.

Quadratic formula to solve the quadratic equation:

To solve the quadratic equation we can use a really simple formula which is given below:

For the first root solve using

x = -b + (b^2 - 4ac)/2a

For the second root solve using

x = -b - (b^2 - 4ac)/2a

Where a,b and c are the constants from the quadratic equation given above.