# Quadratic Equation

*An equation of the form * *ax*^{2}+ bx + c = 0*, where **a**, **b**, **c **are real numbers and **a **≠ **0, is called a quadratic equation in **x**.*

*An equation of the form*

*ax*

^{2}+ bx + c = 0*, where*

*a*

*,*

*b*

*,*

*c*

*are real numbers and*

*a*

*≠*

*0, is called a quadratic equation in*

*x*

*.*

Any equation of the form *p*(*x*) = 0, where *p*(*x*) is polynomial of degree 2, is a quadratic equation.

But when we write the terms of *p*(*x*) in descending order of their degrees, then we get the standard form of the equation.

That is, , standard form of a quadratic equation and

That is, *ax ^{2}+ bx + c = 0*, a ≠ 0 is called the standard form of a quadratic equation and

y = *ax ^{2}+ bx + c * is called a quadratic function.

**A quadratic equation has**

maximum two roots.

maximum two roots.

**• A real number α is called a root of the**

quadratic equation *ax*^{2}+ bx + c = 0, a ≠ 0,

quadratic equation

*ax*, a ≠ 0,

^{2}+ bx + c = 0** if aα**^{2}+ bα + c = 0,

*+ bα + c = 0,*

^{2}**v Any quadratic equation can have at most two roots.**

**Note : If α is a root of ***ax*^{2}+ bx + c = 0, then we say that

*ax*, then we say that

^{2}+ bx + c = 0**(i) x = α satisfies the equation ***ax*^{2}+ bx + c = 0 or

*ax*or

^{2}+ bx + c = 0** (ii) x = α is a solution of the equation ***ax*^{2}+ bx + c = 0

*ax*

^{2}+ bx + c = 0**• The roots of a quadratic equation ***ax*^{2}+ bx + c = 0 are called the zeros of the polynomial *ax*^{2}+ bx + c

*ax*are called the zeros of the polynomial

^{2}+ bx + c = 0*ax*

^{2}+ bx + c