Quadratic Equation

Annotations:

• Roots of a Quadratic Equation Quadratic Equation Polynomial Equation Degree of a Polynomial Complex Polynomial: Real Polynomial:

1. Solution of Quadratic Equation
   1. Factorization Method:
      1. Let ax2 + bx + c = α(x – α) (x – β) = O. Then, x = α and x = β will satisfy the given equation.
   2. Direct Formula
      1. Quadratic equation ax2 + bx + c = 0 (a ≠ 0) has two roots,
2. Nature of Roots
   1. Let quadratic equation be ax2 + bx + c = 0, whose discriminant is D. (i) For ax2 + bx + c = 0; a, b , C ∈ R and a ≠ 0,
      1. (a) D < => Complex roots (b) D > 0 => Real and distinct roots (c) D = 0 => Real and equal roots as α = β = – b/2a