In a particular number system the cubic equation X^3+bX^2+cX-190 has roots 5,8 and 9.What is the base of the no system?
(x-5)(x-8)(x-9) = 0
$\therefore$ x3 - 12x2 +67x -360 = 0
Now, comparing this equation with original, we get (190)y = (360)10 where, y is the new base
$\therefore$ y2 + 9y = 360
$\therefore$ y=-24 or y=15
we get y=15.