Quadratic Equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form

${\displaystyle ax^{2}+bx+c=0,}$

where x represents an unknown, and a, b, and c represent known numbers, with a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ${\displaystyle ax^{2}}$ term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.^[1]

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of its left-hand side. A quadratic equation has at most two solutions. If there is no real solution, there are two complex solutions. If there is only one solution, one says that it is a double root. So a quadratic equation has always two roots, if complex roots are considered, and if a double root is counted for two. If the two solutions are denoted r and s (possibly equal), one has

${\displaystyle ax^{2}+bx+c=a(x-r)(x-s).}$

Thus, the process of solving a quadratic equation is also called factorizing or factoring. Completing the square is the standard method for that, which results in the quadratic formula, which express the solutions in terms of a, b, and c. Graphing may also be used for getting an approximate value of the solutions. Solutions to problems that may be expressed in terms of quadratic equations were known as early as 2000 BC.

Because the quadratic equation involves only one unknown, it is called "univariate". The quadratic equation only contains powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two.

===============================================================================

NOW IF YOU ARE SOLVING 

BEST REVISION BOOK OF MATHEMATICS BY ER. SHAMBHU KUMAR BELOW LINK MAY BE USEFUL TO YOU.