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प्रश्न
Determine the nature of root of the quadratic equation.
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
उत्तर
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
In order to find the nature of the roots we need to find the discriminant.
D = b2 - 4ac
\[a = \sqrt{3}, b = \sqrt{2}, c = - 2\sqrt{3}\]
\[D = \left( \sqrt{2} \right)^2 - 4 \times \sqrt{3} \times \left( - 2\sqrt{3} \right)\]
= 2 + 8 (3)
= 2 + 24
= 26 > 0
Since, the D > 0 so, real and unequal root.
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