3.3 WORKING WITH POLYNOMIALS

You have already learned how to find the zeroes of a linear polynomial.

For example, if k is a zero of p(x) = 2x + 5, then p(k) =0 gives 2k +5 = 0 Therefore; k = -5/2

In general, if k is a zero of p(x) = ax+b (a not equal to 0), then p(k) = ak + b = 0,

Therefore k = -b/a,or the zero of the linear polynomial ax + b is -b/a

Thus, the zero of a linear polynomial is related to its coefficients, including the constant term.

Are the zeroes of higher degree polynomials also related to their coefficients? Think about this and discuss with friends. We will come to this later.

You know that a real number k is a zero of the polynomial p(x) if p(k) = 0. Let us see the graphical representations of linear and quadratic polynomials and the geometrical meaning of their zeroes.

Consider first a linear polynomial ax + b (a not equal to 0). You have studied in Class-IX that the graph of y = ax + b is a straight line. For example, the graph of y = 2x + 3 is a straight line intersectingthe Y-axis at (0, 3) and it also passes through the points (–2, –1) and (2, 7).