"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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Accepted Answer

"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"

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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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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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 :