SOLUTION: 5.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]

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 5.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]      Log On

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Question 31503: 5.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) About Me  (Show Source):
You can put this solution on YOUR website!
I DONT KNOW YOUR COURSE OF STUDY AND BACK GROUND KNOWLEDGE.I HOPE YOU KNOW CALCULUS AND ROLLE'S THEOREM.I AM ANSWERING ON THAT BASIS
CONSIDER F(X)=AX^3+BX^2+CX.....
WE HAVE
F(0)=A*0^3+B*0^2+C*0=0
F(1)=A*1^3+B*1^2+C*1=A+B+C=0..AS GIVEN....SO AS PER ROLLE'S THEOREM
WHEN A CONTINUOUSLY VARYING FUNCTION HAS 2 ZEROES AT BOTH ENDS OF AN INTERVAL...THEN ITS DERIVATIVE WILL HAVE A ZERO AT ONE POINT WITHIN THE INTERVAL.HENCE
DF/DX=3A*X^2+2B*X+C=0 BETWEEN X=0 AND X=1
SO B IS THE ANSWER