Review question

# What can we say if the roots of a cubic are in arithmetic progression? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6276

## Question

1. Given that the roots of the equation $x^3+px^2+qx+r=0$ are three consecutive terms of an arithmetic progression, show that$2p^3 + 27r = 9pq.$
2. Given that the roots of the equation $x^3+px^2+qx+r=0$ are three consecutive terms of a geometric progression, find a condition that $p$, $q$ and $r$ must satisfy.