Obtain the roots of the following quadratic e | vedclass

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Question

(B) For the quadratic equation $ax^{2} + bx + c = 0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Given equation: $2x^{2} + 5\s

Vedclass · Accepted Answer

$-\sqrt{3}, -\frac{\sqrt{3}}{2}$

Vedclass · Answer

(B) For the quadratic equation $ax^{2} + bx + c = 0$,the quadratic formula is $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Given equation: $2x^{2} + 5\sqrt{3}x + 6 = 0$.Here,$a = 2$,$b = 5\sqrt{3}$,and $c = 6$.First,calculate the discriminant $D = b^{2} - 4ac = (5\sqrt{3})^{2} - 4(2)(6) = (25 	imes 3) - 48 = 75 - 48 = 27$.Now,apply the formula: $x = \frac{-5\sqrt{3} \pm \sqrt{27}}{2(2)} = \frac{-5\sqrt{3} \pm 3\sqrt{3}}{4}$.Case $1$: $x = \frac{-5\sqrt{3} + 3\sqrt{3}}{4} = \frac{-2\sqrt{3}}{4} = -\frac{\sqrt{3}}{2}$.Case $2$: $x = \frac{-5\sqrt{3} - 3\sqrt{3}}{4} = \frac{-8\sqrt{3}}{4} = -2\sqrt{3}$.Wait,checking the options provided,the correct roots are $-\frac{\sqrt{3}}{2}$ and $-2\sqrt{3}$. Since this matches the calculation,the correct option is $B$.

Obtain the roots of the following quadratic equation by using the quadratic formula: $2x^{2} + 5\sqrt{3}x + 6 = 0$.

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