Question

If the zeroes of the polynomial 2x3 – 15x2 + 37x – 30 are a – b, a, a + b, find all the zeroes

Answer 1

or,Let 'a-d','a','a+d' are the 3 zeroes of an A.P.
a-d+a+a+d=-(-15)/2=15/2

3a=15/2
or,a=5/2-----(i)

(a-d)a(a+d)=-(-30)/2
or,a(a²-d²)=15
using (i), we get
(5/2)(25/4-d²)=15
or,25/4-d²=6
or,-d²=6-25/4
or,-d²=-(25/4-6)
or,d²=25/4-6
or,d²=1/4
or,d=±1/2

The zeroes are
(5/2-½),5/2,(5/2+½)
or,2,5/2,3