In elementary mathematics, one will come across a polynomial equation of the second degree which are called quadratic equations.Here's the general form of a quadratic equation:
Where a ≠ 0 (The equation will become linear instead)
In high-schools, students are generally given the quadratic formula to solve the equation. The answer for the solved equation are called the roots of the quadratic equation. The solutions can be real or complex and there are two solutions to each quadratic equation.
The formula is given as:
Here, we will go through the derivations to the formula.
We begin as the standard form of a quadratic equation:
Moving the last term to the opposite side and dividing the terms with a;
By applying completion of squares;
rearranging the equation we finally get;