the x -axis at one point only. (ii) The number of zeroes is as the graph intersects the x -axis at two points. (iii) The number of zeroes is . (Why?) (iv) The number of zeroes is .
(Why?) (v) The number of zeroes is . (Why?) (vi) The number of zeroes is . (Why?) EXERCISE . .
The graphs of y = p ( x ) are given in Fig. . below, for some polynomials p ( x ). Find the number of zeroes of p ( x ), in each case.
Fig. . . Relationship between Zeroes and Coefficients of a Polynomial You have already seen that zero of a linear polynomial ax + b is .
We will now try to answer the question raised in Section . regarding the relationship between zeroes and coefficients of a quadratic polynomial. For this, let us take a quadratic polynomial, say p ( x ) = x – x + . In Class IX, you have learnt how to factorise quadratic polynomials by splitting the middle term.
So, here we need to split the middle term ‘– x ’ as a sum of two terms, whose product is × x = x . So, we write x – x + = x – x – x + = x ( x – ) – ( x – ) = ( x – )( x – ) = ( x – )( x – ) So, the value of p ( x ) = x – x + is zero when x – = or x – = , i.e., when x = or x = . So, the zeroes of x – x + are and . Observe that : Sum of its zeroes ( ) ) Product of its zeroes = Let us take one more quadratic polynomial, say, p ( x