Question

Find the relation between p,q and r if the roots of the cubic equation x^3 -px^2+qx -r =0 are such that they are in AP

Answer 1

say the roots are \(\alpha, ~\alpha + d,~ \alpha + 2d\)

Answer 2

sum of roots = p
sum of product of pairs of roots = q
product of roots = r

Answer 3

ok....

Answer 4

we get 3 equations from above^

Answer 5

yes

Answer 6

we need to eliminate \(\alpha, ~ d\) from them and get a relation in terms of p, q, r i guess..

Answer 7

wait let me type the equations

Answer 8

k

Answer 9

the roots of a cubic equation vary with constant difference?

Answer 10

a,a+d,a+2d? is this always true

Answer 11

if 3 roots exist