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2015-06-10T18:48:09+08:00

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Please note that a quadratic equation has the form ax²+bx+c=0

Δ refers to the discriminant which is under the squareroot sign in the quadratic equation which is b²-4ac

Case 1. Δ≥0, the roots are real

      1.1 Δ>0, there are 2 real solutions 
This means b²>4ac. We can simply give x²+3x+2. That is  (x+1)(x+2). And (x+1)(x+3) = x
²+4x+3

      1.2 Δ=0, there is only one root
This would mean b²=4ac. We can simply give (x+1)² or x²+2x+1 and (x+2)
² or x²+2x+4

For Case 1.2, it is like this since if we check the quadratic formula:
-b ± √0 = -b 
    2a       2a

Case 2. Δ<0, there are no real solutions.
Since we would need to get the squareroot of a negative value, which is imaginary.

This would mean b²<4ac. To give an easy example we let a=b=c=1 so x²+x+1 and a=b=1 , c=2; x
²+x+2.
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