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b^2 – 4ac >0 then the roots are real and distinct.

b^2 – 4ac =0 then the roots are real and equal.

b^2 – 4ac <0 then the roots are unreal.

Note : 1. If b^2 – 4ac is a perfect square, the roots are rational and distinct.

2. If b^2 – 4ac is not a perfect square, the roots are irrational and distinct.

The idea may be taught through practice in writing.

34. Relation between the roots
    Let ax^2 + bx + c = 0 be any given quadratic equation. Solving of the equation will lead
    to the two roots which are,

2a

and b-^ b -4ac

2 a

α=−b+^ b^2 −^4 ac β=−^2

Note that α^ +^ β^ =^ - ab^ and^ α^ β^ =^ ac

Also, if the roots of an equation are known then the equation can be found using the

formula, x^2 - (sum of the roots) x + (product of the roots) = 0

The idea may be taught by providing braille text.