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.
- If b^2 – 4ac is not a perfect square, the roots are irrational and distinct.
The idea may be taught through practice in writing.
- 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.