ax2 + bx + c = 0 [a â 0 ] (1)
If and Ã be the roots of the equation (1), then
= and Ã =
Now, suppose that a, b and c are real and rational. Then, the nature of the roots and Ã of
equation (1) is determinedby the expression (b2 â 4ac) under the radical sign.
Therefore (b2 â 4ac) is known as the Discriminant of equation (1). Referred to this discriminant following conclusions can be drawn about the nature of roots and Ã of equation (1):
1. If discriminant is positive (that is, if b2 â 4ac > 0), then the roots and Ã of equation (1) are real andunequal.
Now, here if c is < 0 it means it is a negative digit then discriminant (b2-4ac) becomes positive. Hence the nature of roots will either follow point (1) or point(4) mentioned above.