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 $y=x$, then the possible values of $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are :
Correct Option: 1
Solution:
$2=a+b+c \ldots \ldots(i)$
$\frac{d y}{d x}=2 a x+\left.b \Rightarrow \frac{d y}{d x}\right|_{(0,0)}=1$
$\Rightarrow b=1 \Rightarrow a+c=1$
$(0,0)$ lie on curve
$\therefore \mathrm{c}=0, \mathrm{a}=1$