Question 31497: Which of the below option's are right?
If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast one root in [-1,0]
B.atleast one root in [0,1]
C.atleast one root in [-1,1]
D.atleast one root in [0,2]
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! If a+b+c=0,then 3a*x*x+2b*x+c=0 has
A.atleast one root in [-1,0]
B.atleast one root in [0,1]
C.atleast one root in [-1,1]
D.atleast one root in [0,2]
CONSIDER F(X)=AX^3+BX^2+CX...
F(0)=0
F(1)=A+B+C=0...... GIVEN
HENCE F(X) HASS 2 ZEROS AT EITHER END OF THE INTERVAL [0,1]
DIFFERENTIATING F(X)... W.R.T.X,WE GET
DF/DX=3AX^2+2BX+C....AS PER RTO;;ES THEOREM THIS MUST HAVE A ZERO IN THE INTERVAL [0,1]................SO...............B..IS CORRECT
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