Quadratic Equations and the Discriminant

A quadratic equation is of the form

                        ax² + bx +c = 0

    1.    The highest power of the equation is two.

    2.    a≠ 0

    3.    a is the coefficient of x²

    4.    b is the coefficient of x

    5.    c is the constant term

    6.    There are two roots of quadratic equation. Root means the value of x for which the expression                      
                                  ax² + bx +c becomes 0.

Solving the quadratic equation using

v    1.    Factor method

    In factor method we try to write the equation in its factor form and then from the factors we can  
     get the roots of the above equation.

     Here we try to write the quadratic expression ax² + bx +c =0 as (x + α)(x + β) =0

                  Where α and β are the roots of the quadratic equation,

       2.    Formula method

      The roots of the quadratics equations are

       α(first root) = (-b+√b² -4ac)/2a

          and

      β(second root) = (-b-√b² -4ac)/2a

  Sum and product of roots

  The relations between the coefficient of the quadratic equation and the roots of the equations are

       1.    Sum of roots of quadratic equation = -b/a

       2.    Product of the roots of quadratic equations = c/a

 Discriminant and nature of the roots

 The discriminant (D) of a quadratic equation is defined as

                        D = √b² -4ac

The relation between the discriminant and the nature of the roots is

        1.    If  √b² -4ac= o then both the roots are real and equal

        2.    If √b² -4ac > 0 then both the roots are real and unequal

        3.    If √b² -4ac< 0 the both the roots are imaginary and unequal