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Quadratic Equations
Previous Year Questions (2022-2024)
Year 2022
- Find two consecutive positive integers whose product is 306.
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Let integers be x, x+1\nx(x+1) = 306 => x2 + x - 306 = 0\n=> (x+18)(x-17) = 0\nx = 17 (positive)\nIntegers: 17, 18 - A train travels 480 km at uniform speed. If speed were 8 km/h less, it would take 3 hours more. Find speed of train.
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Let speed = x km/h, time = 480x hours\nNew speed = x-8, new time = 480x-8\n480x-8 - 480x = 3\n=> 480x - 480(x-8) = 3x(x-8)\n=> 3840 = 3x2 - 24x\n=> x2 - 8x - 1280 = 0\n=> (x-40)(x+32) = 0\nx = 40 km/h
Year 2023
- Solve: 1x-2 + 2x-1 = 6x, x != 0,1,2.
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1x-2 + 2x-1 = 6x\n=> x(x-1) + 2x(x-2) = 6(x-1)(x-2)\n=> x2 - x + 2x2 - 4x = 6(x2 - 3x + 2)\n=> 3x2 - 5x = 6x2 - 18x + 12\n=> 3x2 - 13x + 12 = 0\n=> (3x-4)(x-3) = 0\nx = 43 or x = 3 - Find two consecutive positive integers whose product is 306.
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Let integers be x, x+1\nx(x+1) = 306 => x2 + x - 306 = 0\n=> (x+18)(x-17) = 0\nx = 17 (positive)\nIntegers: 17, 18
Year 2024
- A train travels 480 km at uniform speed. If speed were 8 km/h less, it would take 3 hours more. Find speed of train.
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Let speed = x km/h, time = 480x hours\nNew speed = x-8, new time = 480x-8\n480x-8 - 480x = 3\n=> 480x - 480(x-8) = 3x(x-8)\n=> 3840 = 3x2 - 24x\n=> x2 - 8x - 1280 = 0\n=> (x-40)(x+32) = 0\nx = 40 km/h - Solve: 1x-2 + 2x-1 = 6x, x != 0,1,2.
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1x-2 + 2x-1 = 6x\n=> x(x-1) + 2x(x-2) = 6(x-1)(x-2)\n=> x2 - x + 2x2 - 4x = 6(x2 - 3x + 2)\n=> 3x2 - 5x = 6x2 - 18x + 12\n=> 3x2 - 13x + 12 = 0\n=> (3x-4)(x-3) = 0\nx = 43 or x = 3