If the line y = 2x touches the curve y = ax^2 + bx + c

If the line y = 2x touches the curve y = ax^2 + bx + c at the point where x = 1 and the curve passes through the point (-1, 0), then the values of a, b, c are

$a = \frac{1}{2} b = 1, c = \frac{1}{2}$

$a = 1, b = \frac{1}{2} c = \frac{1}{2}$

$a = \frac{1}{2}, b = \frac{1}{2}, c = 1$

D. $a = 1, b = 2, c = - 1$

Please scroll down to see the correct answer and solution guide.

Right Answer is: A

SOLUTION

The given curve is $y = a x^{2} + b x + c$ ...(1)
Since the point (-1, 0) lie on it.
∴ a - b + c = 0 ...(2)
Also, y = 2x is a tangent to (1) at x = 1, so that y = 2,
Since the point (1, 2) lies on equation (1), ...(3)
$∴$ a + b + c =2
Also ${[\frac{d y}{d x}]}_{(1, 2)} = (2 a x + b)_{12} = 2. ∴ 2 a + b = 2..... (4)$
On solving equation (2), (3) and (4), we get
$a = \frac{1}{2}, b = 1, c = \frac{1}{2}$
Hence (a) is the correct answer

If the line y = 2x touches the curve y = ax^2 + bx + c

Right Answer is: A

SOLUTION

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