INTRODUCTION:

INTRODUCTION:
Quadratic Polynomial:
A polynomial, whose degree is 2, is called a quadratic polynomial. It is in the form of
p(x) = ax² + bx + c , where a ≠ 0

Quadratic Equation:
When we equate the quadratic polynomial to zero then it is called a Quadratic Equation i.e. if
p(x) = 0, then it is known as Quadratic Equation.
Standard form of Quadratic Equation:
ax² + bx + c
where a, b, c are the real numbers and a ≠ 0
Types of Quadratic Equations:

1. Complete Quadratic Equation ax² + bx + c = 0, where a ≠ 0, b ≠ 0, c ≠ 0
2. Pure Quadratic Equation ax² = 0, where a ≠ 0, b = 0, c = 0

Any equation needs to be simplified before we decide it is a quadratic equation or not.
There are three methods to solve a quadratic equation.

1. Factorisation
2. Completing the square
3. Quadratic formula.

A quadratic equation in the variable x is of the form x² + bx + c , where a ≠ 0 where a, b, c are real numbers and a ≠ 0.
 A real number α is a root of the quadratic equation x²+bx+c ,where a ≠ 0 if aα² + bα + c = 0.
The zeroes of the quadratic polynomial x² + bx + c , and the roots of the quadratic equation ax²+bx+c , = 0 are the same.
 If we can factorise x² + bx + c , where a ≠ 0 into a product of two linear factors, then the roots of the quadratic equation ax²+bx+c = 0,can be found by equating each factor to zero.
 Quadratic formula: The roots of a quadratic equation ax² + bx + c = 0,are given by,
provided b² – 4ac ≥ 0.
 A quadratic equation ax² + bx + c = 0, has
(i) two distinct real roots, if b² – 4ac > 0,
(ii) two equal roots (i.e., coincident roots), if b² – 4ac = 0, 
(iii) no real roots, if b² – 4ac < 0.