If the curve y = ax2 + bx + c, x\[ \in \]R, passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are :
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Official solution
Given curve y = ax2 + bx + c, x\[ \in \]R
This curve passes through the point (1, 2)
\[ \therefore \] 2=a+b+c ..... (i)
Given, slope of tangent at origin is 1
\[ \therefore \] \[{{dy} \over {dx}} = 2ax + b \Rightarrow {\left. {{{dy} \over {dx}}} \right|_{(0,0)}} = 1\]
\[ \Rightarrow b = 1 \Rightarrow a + c = 1\]
(0, 0) lie on curve
\[ \therefore \] c = 0, a = 1