Solution : We have x + x + = ( x + )( x + ) So, the value of x + x + is zero when x + = or x + = , i.e., when x = – or x = – . Therefore, the zeroes of x + x + are – and – . Now, sum of zeroes = ( ) –(Coefficient of ) , – (– ) – ( ) product of zeroes = ( ) Example : Find the zeroes of the polynomial x – and verify the relationship between the zeroes and the coefficients. Solution : Recall the identity a – b = ( a – b )( a + b ).
Using it, we can write: