(Constant term) Thus, the zero of a linear polynomial is related to its coefficients. Does this happen in the case of other polynomials too? For example, are the zeroes of a quadratic polynomial also related to its coefficients? In this chapter, we will try to answer these questions.
We will also study the division algorithm for polynomials. . Geometrical Meaning of the Zeroes of a Polynomial You know that a real number k is a zero of the polynomial p ( x ) if p ( k ) = . But why are the zeroes of a polynomial so important?
To answer this, first we will see the geometrical representations of linear and quadratic polynomials and the geometrical meaning of their zeroes. Consider first a linear polynomial ax + b , a . You have studied in Class IX that the graph of y = ax + b is a straight line. For example, the graph of y = x + is a straight line passing through the points (– , – ) and ( , ).
– y = x + – From Fig. . , you can see that the graph of y = x + intersects the x -axis mid-way between x = – and x = – , that is, at the point , You also know that the zero of x + is . Thus, the zero of the polynomial x + is the x -coordinate of the point where the graph of y = x + intersects the x -axis.
In general, for a linear polynomial ax + b , a , the graph of y = ax + b is a straight line which intersects the x -axis at exactly one point, namely, , Therefore, the linear polynomial ax + b , a , has exactly one zero, namely, the x -coordinate of the point where the graph of y = ax + b intersects the x -axis. Now, let us look for the geometrical meaning of