If 2a+3b+6c=0, the at least one root of the equation ax2+bx+c=0 lies in the interval 

If 2a+3b+6c=0, the at least one root of the equation ax2+bx+c=0 lies in the interval 

  1. A

    (0,1)

  2. B

    (1, 2)

  3. C

    (2, 3)

  4. D

    none of these

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    Solution:

    Consider the function 

    f(x)=ax33+bx22+cx

    We find that f(0)=0 and,

    f(1)=a3+b2+c=2a+3b+6c6=06=0[2a+3b+6c=0]

    Therefore, 0 and 1 are roots of the polynomial f (x). 

    Consequently, there exists at least one root of the polynomial

    f(x)=ax2+bx+c lying between 0 and 1.

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