Find the condition which must be satisfied by the coefficients of the polynomial f(x)=x3-(x2+ mx-n. Given that the sum of the two zeroes is zero.
Solution Let a, B and y be the zeroes of the polynomial f(x) such that a+B=0. Coefficient of x2 Now, a +B+ y = Coefficient of x Since, y is a zero of the polynomial f(x). Therefore, f(y)=0 = y3 –ly+ my - n = 0 [: y = l] = P3 - 13 + ml - n=0= ml=n This is the required condition.
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