∵a1,a2,a3,a4 ∴a2=p−3d,a2=p−d,a3=p+d and a4=p+3d Where d>0 ∵|f(ai)|=500 ⇒|9d2−q|=500 and |d2−q|=500 either 9d2−q=d2−q ⇒d=0 not acceptable ∴9d2−q=q−d2 ∴5d2−q=0 Roots of f(x)=0 are p+√q and p−√q ∴ absolute difference between roots =|2√q|=50