minima doubt!!!!!!!!

if 2a+3b+6c=0, then atleast one root of the equation ax^2 +bx +c=0 lies in the interval:
1) 0,1
2)1,2
3)2,3
4)1,3

BHAI 4 THE 2ND ONE
U HAVE TO INTEGRATE THIS FUNCTION TO FIND A NEW FUNCTION SO AS TO FIND THE INTERVAL

ON INTEGRATING U GET

ax³/3+bx²/2+cx=0

u get

2ax³+3bx²+6cx=0

now x=1 satisfies the given relation
and at x=0 c=0

soits 1 root must lie between (0,1)

1=2/b+3/a ..
==> (2/b+3/a)/2 ≥ √6/ab (AM-GM)
==> 1/2 ≥ √6/ab
==> 1/4≥ 6/ab
==> ab ≥ 24

and at x=0 c=0

soits 1 root must lie between (0,1)

manipal pls explain this sentence.[2]