A quadratic equation takes the form of ax² + bx + c = 0. It may have two equal roots, two distinct roots or no roots at all.
The value of 'a' determines the shape of graph - upside down or same way up; 'c' determines the point that it crosses the y-axis.
The value of b² - 4ac, also known as Discriminant, determines whether there are roots for a quadratic equation.
If D is negative, there are no real solutions.
If D is zero or positive there are real solutions.

This programme was using AJAX technology; the programme solves the equation at the click of a button, without taking the contents of the whole page through the internet while clogging up the arteries of the network unnecessarily. It takes only the bear minimum of data needed for the calculation. The absence of flicker or refreshing shows the power of the new technology.

Question One:

x² -x - 6 = 0

Question Two:

x² -6x + 8 = 0

Question Three:

x² -6x + 9 = 0