Notes for Quadratic Equations

A Polynomial of the form *p(x) = ax*^{2} + bx + c, where *a* 0 and *a*, *b*, *c* are real numbers and *x* is a real variable is called a **quadratic polynomial**.

An equation *p*(*x*) = 0, where *p*(*x*) is a quadratic polynomial is called a quadratic equation i.e. *ax*^{2} + *bx* + *c* = 0, *a* 0.

Those values of *x* for which *ax*^{2} + *bx *+ *c* = 0 is satisfied are called zeros of quadratic equation.

by putting *b* = 0 in *ax*^{2} + *bx* + *c* = 0

If α, β are the zeros of the polynomial *ax*^{2} + *bx *+ *c*. Then α, β are called roots of corresponding equation

⇒ *p*(α) = *p*(β) = 0

i.e. *aα*^{2} + *bα* + *c* = 0

and *a*β^{2} + *b*β + *c* = 0

Pure quadratic *ax*^{2} + *c* = 0 can be solved by any one of the following methods:

Affected quadratic equation can be solved by any one of the following method:

The quadratic formula or Sridharacharya’s formula to find the roots of *ax*^{2} + *bx* + *c* = 0 is