Question

If zeros of the polynomial f(x) = x³ -3px² + qx - r are in A.P., then *

Answer 1

Answer:

x³-3px²+qx-r are in A.P

let a,a+d,a-d, are zeroes

sum of zeroes is a+a-d+a+d=3p

3a=3p

a=p

p is one zero

f(p)=p³-3p(p²)+q(p)-r=0

p³-3p³+qp-r=0

2p³+r=qp