Quadratic Equations

A quadratic equation or second degree equation in $$x$$ is written in standard form as
\[a{x^2} + bx + c = 0\] with $$a \ne 0$$

If $$a = 0$$, then the quadratic equation reduces to linear equation, i.e., $$bx + c = 0$$.

The word quadratic is derived from the Latin word quadratum which means “related to two or to make square”.



  1. $$2x + 6{x^2} + 1 = 0$$
  2. $$3{x^2} = 12$$
  3. $$2{x^2} – 1 = 5x + 9$$


Solution of Quadratic Equations

The process of finding the values of unknown quantity (variables) which satisfy the given quadratic equation is called the solution of the quadratic equation. The values which satisfy the quadratic equation are called the roots of the quadratic equation. A set consisting of all roots of the quadratic equation is called a solution set.

We discuss three methods for solving quadratic equations: factorization, completing the square and using the quadratic formula. In the following tutorials we explain all three methods.