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P1 Topic 2: Algebra
The discriminant backmore
For any quadratic function ax2+bx+c the function
is called the discriminant.
For example:
x2+4x+1 has discriminant 16 - 4 = 12
x2+6x+9 has discriminant 36 - 36 = 0
x2-4x+3 has discriminant 16 - 12 = 4
x2-2x-2 has discriminant 4 + 8 = 12
x2+12x+40 has discriminant 144 - 160 = -16
Use the interactive display. Change the values of a, b and c and observe what happens to the position of the quadratic curve y = ax2+bx+c. How many times does the curve cross the x-axis? This tells you how many solutions the equation ax2+bx+c = 0 has.

What happens in each of these cases:
When b²-4ac>0
When b²-4ac<0
When b²-4ac=0 ?
a =
b =
c =

Summary
Any quadratic function ax2+ bx + c has discriminant b²-4ac. The quadratic equation ax2+ bx + c = 0 has
  • two roots when b²-4ac > 0, and the curve will cross the x axis twice.
  • one root when b²-4ac = 0, and the curve will cross the x axis once.
  • no roots when b²-4ac < 0, and the curve will not cross the x axis at all.
JavaMath interactive graphs Based on free Java applets from JavaMath