Question

Find the condition to be satisfied by the coefficient of factor equal to x^3-px^2+qx-r when sum of its zeroes is zero

Answer 1

f(x)=x³-px²+qx-r.
The standard form of a cubic equation is:
x³-(a+b+c)x²+(ab+bc+ca)x-abc=0.
Comparing this equation with the given polynomial:
We find:
(a+b+c)=3p
given(a+b+c)=0 {sum of roots=0}
so 3p=0
p=0