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 $y=a{x}^{2}+bx+c$ passes through the point (1, 2) such that the slope of the tangent at the origin is equal to 1, then

1. A

2. B

$\left(1,1,0\right)$

3. C

$\left(\frac{1}{2},1,1\right)$

4. D

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### Solution:

It is given that $y=a{x}^{2}+bx+c$ passes through
and . Therefore,

and  and

Now, $\begin{array}{r}y=a{x}^{2}+bx+c\\ ⇒\frac{dy}{dx}=2ax+b⇒{\left(\frac{dy}{dx}\right)}_{\left(0,0\right)}=b\end{array}$

But, ${\left(\frac{dy}{dx}\right)}_{\left(0,0\right)}=1$

But,  Therefore, . Hence,

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