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Question
Solve the following equation : `|(1, 4, 20),(1, -2, 5),(1, 2x, 5x^2)| = 0`
Solution
`|(1, 4, 20),(1, -2, 5),(1, 2x, 5x^2)| = 0`
∴ `1|(-2, 5),(2x, 5x^2)| -4|(1, 5),(1, 5x^2)| + 20|(1, -2),(1, 2x)|` = 0
∴ 1(– 10x2 –10x) – 4(5x2 – 5) + 20(2x + 2) = 0
∴ – 10x2 – 10x – 20x2 + 20 + 40x + 40 = 0
∴ – 30x2 + 30x + 60 = 0
∴ x2 – x –2 = 0 ...[Dividing throughout by (– 30)]
∴ x2 – 2x + x – 2 = 0
∴ (x – 2)(x + 1) = 0
∴ x – 2 = 0 or x + 1 = 0
∴ x = 2 or x = – 1
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