If the curve y=ax2+bx+c passes through the point (1, 2) such that the slope of the tangent at the origin is equal to 1, then (a, b, c) =

If the curve y=ax2+bx+c passes through the point (1, 2) such that the slope of the tangent at the origin is equal to 1, then (a, b, c) =

  1. A

    12, 1, 0

  2. B

    (1,1,0)

  3. C

    12,1,1

  4. D

    (2,1, 0)

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    Solution:

    It is given that y=ax2+bx+c passes through (1, 2)
    and (0, 0). Therefore,

    2 =a+ b + c and 0= c a+ b = 2 and c = 0

    Now, y=ax2+bx+cdydx=2ax+bdydx(0,0)=b

    But, dydx(0,0)=1

     b=1

    But, a+b = 2. Therefore, a =1. Hence, (a, b, c) =(1, 1, 0).

     

     

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