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Question
Solve: `sqrt(3)x^2 + 10x - 8sqrt(3) = 0`.
Sum
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Solution
`sqrt(3)x^2 + 10x - 8sqrt(3) = 0`
⇒ `sqrt(3)x^2 + 12x - 2x - 8sqrt(3) = 0`
⇒ `sqrt(3)x(x + 4sqrt(3)) - 2(x + 4sqrt(3)) = 0`
⇒ `(x + 4sqrt(3)) (sqrt(3)x - 2) = 0`
⇒ `x + 4sqrt(3) = 0` or `sqrt(3)x - 2 = 0`
⇒ `x = -4sqrt(3)` or `x = 2/sqrt(3) = (2sqrt(3))/3`
Hence, `-4sqrt(3)` and `(2sqrt(3))/3` are the roots of the given equation.
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