In the previous section, we have seen that the roots of the equation ax
2
+ bx + c = 0 are
given by
2
4
2
-± -
=
b b ac
x
a
Now let us try to study the nature of roots.
Remember that zeroes are those points where value of polynomial becomes zero or we
can say that the curve of quadratic polynomial cuts the X-axis.
Similarly, roots of a quadratic equation are those points where the curve cuts the X-axis.
Case-1 : If b
2
- 4ac > 0;
We get two distinct real roots
2
4
2
b b ac
a
-+ -
,
2
4
2
b b ac
In such case if we draw corresponding graph for the given quadratic equation we get the
following types of figures.
Figure shows that the corresponding curve of the quadratic equation cuts the X-axis at two
Case-2 : If b
2
- 4ac = 0
x =
0
2
b
a
- +
So, x = 2
b
a
-
,
2
-b
a
Figure shows that the graph of the quadratic equation touches X-axis at one point.
Case-3 : b
2
- 4ac < 0
There are no real roots. Roots are imaginary.
pgno.124