2. Polynomials

2.1 Introduction and Types of Polynomials

2.2 Geometrical Meaning of the Zeroes of a Polynomial

1. Plotting a linear polynomial in a graph.

2. Plotting a quadratic polynomial in a graph.

3. Plotting a cubic polynomials in a graph.

Example 1:

Look at the graphs in Fig. 2.9 given below. Each is the graph of y = p(x), where p(x) is a polynomial. For each of the graphs, find the number of zeroes of p(x).

EXERCISE 2.1

1. The graph of y = p(x) are gived in Fig. 2.10.below, for some polynomials p(x). Find the number of zeros of p(x), in each case.

2.3. Relationship between Zeroes and Coefficients of a Polynomials.

Example 2:

Find the zeroes of the quadratic polynomials x²+ 7x + 10, and verify the relationship between the zeroes and the coefficients.

Example 3:

Find the zeroes of the polynomials x²- 3, and verify the relationship between the zeroes and the coefficients.

Example 4:

Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively.

Example 5:

Verify that 3, -1, -1/3 are the zeroes of the cubic polynomial p(x) = 3x³ - 5x² - 11x - 3, and then verify the relationship between the zeroes and the coefficients.

Exercise 2.2

1. Find the zeroes of the following quadratic and verify athe relationship between the zeroes and the coefficients.

(i) x² - 2x - 8 (ii) 4s² - 4s + 1 (iii) 6x² -3 - 7x (iv) 4u² + 8u (v) t² - 15 (vi) 3x² - x - 4

2. Find a quadratic polynomial each with the given numbers as the sum and product of it's zeroes respectively.