CBSE Class 10 Answered

If and ß be the roots of the equation (1), then

= and ß =

Now, suppose that a, b and c are real and rational. Then, the nature of the roots and ß of
equation (1) is determinedby the expression (b2 – 4ac) under the radical sign.

Therefore (b² – 4ac) is known as the Discriminant of equation (1). Referred to this discriminant following conclusions can be drawn about the nature of roots and ß of equation (1):

1. If discriminant is positive (that is, if b² – 4ac > 0), then the roots and ß of equation (1) are real andunequal.

2. If discriminant is zero (that is, if b² – 4ac = 0), then the roots and ß of equation (1) are real and equal

3. If discriminant is negative (that is, if b² – 4ac < 0), then the roots and ß of equation (1) are imaginary and unequal

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.

Regards

Team Topperlearning