QUADRATIC EQUATIONS

 Quadratic Equation: Any equation which is in the form of ax² + bx + c = 0.

     where a, b, c ∈ R and a ≠ 0 is called a quadratic equation.

 Notes:

* ax²+bx+c=0 is also considered as the general form of Q.E

* x = (-b ± √b²-4ac)/2a are called the two zeroes (or) Roots.

* b² - 4ac is called the 'Discriminant' and it is denoted by ∆ (delta) or D, i.e

 D = b²-4ac.

* 'Nature' of roots is purely based on Discriminant value.

* If D = 0, then the roots are real and equal.32w1

* If D > 0, then the roots are real and unequal.

* If D < 0, then the roots are imaginary (or) complex (or) no real roots.

* ax² + bx + c = 0 represents a 'parabola'.