MATHS
posted by JASLEEN .
two zeros of cubic polynomial ax^3+3x^2bx6 are 1 and 2. find the third zero and values of a and b

if x=1, then a + 3 + b  6 = 0
a  b = 3
if x=2, then 8a + 12 + 2b  6 = 0
8a  2b = 6
4a  b = 3
subtract them:
3a = 6
a = 2
in ab=3
2b = 3
b = 5
so expression is
2x^3 + 3x^2  5x  6
which is (x+1)(x+2)( ?x + ?)
by common sense, the last bracket must be
(2x 3)
so the third root is x=3/2
check:
(x+1)(x+2)(2x3)
= (x^2 + 3x + 2)(2x3)
= 2x^3  3x^2 + 6x^2  9x + 4x  6
= 2x^3 + 3x^2  5x  6 , all is good