Question

Find the condition that the zeros of the polynomial f(x)=x^3-px^2+qx-r may be in arithmetic progression

Answer 1

x³-(a+b+c)x²+(ab+bc+ca)x-abc=0.
Comparing this equation with the given polynomial:
We find:
3p=-(a-d+a+a+d).
=>3p=-3a
=>p=-a