Let be given by then,
(ii) Also, at x = 0, y = 0, thus the curve passes through the origin.
Now, thus f(x) is increasing in these interval
Also, thus decreasing in (-1, 1).
(iv) Also , at x = -1, changes its sign from + ve to ve
x= - 1 is point of local maxima.
Similarly, x = 1 is point of local minima
Local maximum value,
Local minimum value,
Now, let y = -a
As, evident from the graph, if
Then, f(x) has three real roots and
if then f(x) has one real root.