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Question
Find which of the following equations are quadratic:
(x – 4)(3x + 1) = (3x – 1)(x + 2)
Solution
(x – 4)(3x + 1) = (3x – 1)(x + 2)
`\implies` 3x2 + x – 12x – 4 = 3x2 + 6x – x – 2
`\implies` 3x2 – 11x – 4 = 3x2 + 5x – 2
`\implies` 3x2 – 11x – 4 – 3x2 – 5x + 2 = 0
`\implies` –16x – 2 = 0
`\implies` 16x + 2 = 0; which is not of the form ax2 + bx + c = 0.
∴ Given equation is not a quadratic equation.
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