If the curve y = ax^2 + bx + c passes through (1, 2) and the tangent to this curve at the origin is y = x , then the possible values of a, b, c are: - Mathematics MCQ Mathematics Mock Test - 3 2026 | ExamTest.live

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If the curve y = a x^{2} + b x + c passes through (1, 2) and the tangent to this curve at the origin is y = x, then the possible values of a, b, c are:

Solution & Step-by-step Explanation

1. Curve passes through origin (0, 0) ⟹ 0 = a (0)^{2} + b (0) + c ⟹ c = 0 .2. Tangent at origin is y = x ⟹ Slope \frac{d y}{d x} at (0, 0) is 1 . \frac{d y}{d x} = 2 a x + b . At (0, 0), \frac{d y}{d x} = b ⟹ b = 1 .3. Curve passes through (1, 2) ⟹ 2 = a (1)^{2} + b (1) + c 2 = a + 1 + 0 ⟹ a = 1 .So, a = 1, b = 1, c = 0 .

Try it yourself before checking the explanation above.

If the curve y = a x^{2} + b x + c passes through (1, 2) and the tangent to this curve at the origin is y = x, then the possible values of a, b, c are:

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

a = 1, b = 0, c = 1

a = 1, b = 1, c = 0

a = - 1, b = 1, c = 1

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