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Question
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
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Solution
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3)` = 0.
Here, `a = 2sqrt(3), b = -2sqrt(2) and c = -sqrt(3)`
D = b2 - 4ac
⇒ D - 8 - 4 x 2`sqrt(3) xx- sqrt(3)`
⇒ D = 8 + 24
= 32 > 0
The given equation has real roots.
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