Quadratic Equation Tutorial


Quadratic Equation Real and Double Roots Tutorial.
Quadratic Equation Definition:
        A quadratic equation is a polynomial equation of the second degree. The general form is ax2+bx+c=0, where a ≠0.

Quadratic Equation Formula :
ax2 + bx + c = 0,
where
        a = coefficient of x2
        b = coefficient of x and
        c = constant.
Quadratic Equation solving formula:
x = (- b ±√ b2 - 4 * a * c) / 2 * a

Example 1:  Calculate the roots(x1, x2) of the quadratic equation, x2 + 2x - 8 = 0.

  Step 1:  From the above equation, the value of a = 1, b = 2 and c = - 8.

  Step 2:  To Find X:
           Substitute the values in the formula below
                     x = (- b ±√ b2 - 4 * a * c) / 2 * a

  Step 3:  We get the roots, x = (- 2 ±√ 22 - 4 * 1 * - 8) / 2 * 1
              x = - 4 and x = 2
              which means x1 = - 4 and x2 = 2.

Example 2: Calculate the roots(x1, x2) of the quadratic equation, x2 - 10x + 25 = 0

  Step 1:  From the above equation, the value of a = 1, b = - 10 and c = 25.

  Step 2:  To Find X:
              Substitute the values in the formula below
              x = (- b ±√ b2 - 4 * a * c) / 2 * a

  Step 3:  We get the roots, x = (- 2 ±√ 22 - 4 * 1 * - 8) / 2 * 1
              x = 5 and x = 5
              which means x1 = 5 and x2 = 5.

  Here x = 5 is called the double root. A quadratic will have a double root if the quadratic is a perfect square trinomial.



This tutorial will help you dynamically to find the roots of a quadratic equation.