JEE Advance - Mathematics (1983 - No. 43)

If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has

at least one root in $$\left[ {0,1} \right]$$

one root in $$\left[ {2,3} \right]$$ and the other in $$\left[ {-2,-1} \right]$$