### Theory:

A polynomial of the form $$ax^3 + bx^2 + cx + d$$, $$a \neq 0$$ is a cubic polynomial.

Consider the graph of $$y = 2x^3 - 3x$$.

 $$x$$ $$-2$$ $$-1$$ $$0$$ $$1$$ $$2$$ $$2x^3$$ $$2(-2)^3$$ $$=$$ $$2(-8)$$ $$=$$ $$-16$$ $$2(-1)^3$$ $$=$$ $$2(-1)$$ $$=$$ $$-2$$ $$2(0)^3$$ $$=$$ $$2(0)$$ $$=$$ $$0$$ $$2(1)^3$$ $$=$$ $$2(1)$$ $$=$$ $$2$$ $$2(2)^3$$ $$=$$ $$2(8)$$ $$=$$ $$16$$ $$3x$$ $$3 \times -2$$ $$=$$ $$-6$$ $$3 \times -1$$ $$=$$ $$-3$$ $$3 \times 0$$ $$=$$ $$0$$ $$3 \times 1$$ $$=$$ $$3$$ $$3 \times 2$$ $$=$$ $$6$$ $$2x^2 - 3x$$ $$-16$$ $$+$$ $$6$$ $$=$$ $$-10$$ $$-2$$ $$+$$ $$3$$ $$=$$ $$1$$ $$0$$ $$-$$ $$0$$ $$=$$ $$0$$ $$2$$ $$-$$ $$3$$ $$=$$ $$-1$$ $$16$$ $$-$$ $$6$$ $$=$$ $$10$$ $$y$$ $$=$$ $$2x^2 - 3x$$ $$-10$$ $$1$$ $$0$$ $$-1$$ $$10$$

Join the coordinates $$(-2, -10)$$, $$(-1, 1)$$, $$(0, 0)$$, $$(1, -1)$$ and $$(2, 10)$$ by a smooth curve so as to obtain the graph of $$y = 2x^2 - 3x$$. It is observed that, the graph of the polynomial $$y = 2x^2 - 3x$$ intersects the $$x$$ $$-$$ axis at three points.

Thus, we can say that the zero of a cubic polynomial is the $$x$$ $$-$$ coordinates of the point where the graph of the polynomial intersects the $$x$$ $$-$$ axis.

Let us discuss few cases of graphs of a cubic polynomial.

Case 1: The graph of the cubic polynomial cuts the $$x$$ $$-$$ axis at one point, as shown below. In this case, the number of zeroes of the polynomial is $$1$$.

Case 2: The graph of the cubic polynomial cuts the $$x$$ $$-$$ axis at two points, as shown below. In this case, the number of zeroes of the polynomial is $$2$$.

Case 3: The graph of the cubic polynomial cuts the $$x$$ $$-$$ axis at three points, as shown below. In this case, the number of zeroes of the polynomial is $$3$$.
The cubic polynomial $$ax^3 + bx^2 + cx + d$$, $$a \neq 0$$, has at most three zeroes which is the $$x$$ $$-$$ coordinates of the point where the graph of the polynomial intersects the $$x$$ $$-$$ axis.
Important!
In general, the graph of the polynomial of $$n$$ degree intersects the $$x$$ $$-$$ axis at atmost $$n$$ points.

In other words, the polynomial of $$n$$ degree has atmost $$n$$ zeroes.