Question:
If the curve $y=a x^{2}+b x+c, x \in R$, passes through the point $(1,2)$ and the tangent line to this curve at origin is $\mathrm{y}=\mathrm{x}$, then the possible values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are :
Correct Option: 3,
Solution:
$a+b+c=2$ ................(2)
and $\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right|_{(0,0)}=1$
$2 \mathrm{ax}+\left.\mathrm{b}\right|_{(0,0)}=1$
$\mathrm{b}=1$
Curve passes through origin
So, $\mathrm{c}=0$
and $a=1$
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