Case (iii) : Here, the graph is either completely above the X-axis or completely below the X-axis. So, it does not cut the X-axis at any point.


So, the quadratic polynomial ax2 + bx + c has no zero in this case.

So, you can see geometrically that a quadratic polynomial can have either two distinct zeroes or two equal zeroes (i.e., one zero), or no zero. This also means that a polynomial of degree 2 has atmost two zeroes.

Try This

1. Write three quadratic polynomials that have 2 zeroes each.

2. Write one quadratic polynomial that has one zero.

3. How will you verify if a quadratic polynomial has only one zero?

4. Write three quadratic polynomials that have no zeroes.


3.4.3GEOMETRICAL MEANING OF ZEROES OF A CUBIC POLYNOMIAL

What do you expect the geometrical meaning of the zeroes of a cubic polynomial to be? Let us find out. Consider the cubic polynomial x3 – 4x. To see how the graph of y = x3– 4x looks like, let us list a few values of y corresponding to a few values for x as shown in Table 3.3



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