Question

# 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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