Question

If x=1 and x=2 are zeros of f(x)=3X^3+Ax^2+Bx+2, then the value of A+B is a)1, b)-1, c)9, d)-9, e) cannot be determined

I think it can't be determined but i don't know!

Answer 1

Find A+B in
f(x)=3X^3+Ax^2+Bx+2,

Hints:
1. two of the roots are 1 and 2, then two of the factors are (x-1) and (x-2)
2. the third root must be of the form
(3x±1) to satisfy the coefficient 3x^3 and the constant term.
3. Determine the sign of the factor in (2).
4. Expand
(x-1)(x-2)(3x±1)
to find A and B, and hence A+B.