The roots of the equation x^2 + 2sqrt{3}x + 3 | vedclass

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(C) Given the quadratic equation $x^2 + 2\sqrt{3}x + 3 = 0$.Comparing this with $ax^2 + bx + c = 0$,we get $a = 1, b = 2\sqrt{3}, c = 3$.The discrimin

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Irrational and equal

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(C) Given the quadratic equation $x^2 + 2\sqrt{3}x + 3 = 0$.Comparing this with $ax^2 + bx + c = 0$,we get $a = 1, b = 2\sqrt{3}, c = 3$.The discriminant $D = b^2 - 4ac$ is calculated as:$D = (2\sqrt{3})^2 - 4(1)(3)$$D = 12 - 12 = 0$.Since $D = 0$,the roots are real and equal.Further,the roots are given by $x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-2\sqrt{3} \pm 0}{2(1)} = -\sqrt{3}$.Since $-\sqrt{3}$ is an irrational number,the roots are irrational and equal.

The roots of the equation $x^2 + 2\sqrt{3}x + 3 = 0$ are

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