Solve sqrt{5} x^{2} + x + sqrt{5} = 0. | vedclass

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Question

(A) Given the quadratic equation $\sqrt{5} x^{2} + x + \sqrt{5} = 0$. Comparing this with $ax^{2} + bx + c = 0$,we have $a = \sqrt{5}$,$b = 1$,and $c

Vedclass · Accepted Answer

$\frac{-1 \pm \sqrt{19} i}{2 \sqrt{5}}$

Vedclass · Answer

(A) Given the quadratic equation $\sqrt{5} x^{2} + x + \sqrt{5} = 0$. Comparing this with $ax^{2} + bx + c = 0$,we have $a = \sqrt{5}$,$b = 1$,and $c = \sqrt{5}$. The discriminant $D = b^{2} - 4ac$ is calculated as: $D = (1)^{2} - 4(\sqrt{5})(\sqrt{5}) = 1 - 4(5) = 1 - 20 = -19$. The roots are given by the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$. Substituting the values,we get $x = \frac{-1 \pm \sqrt{-19}}{2\sqrt{5}}$. Since $\sqrt{-1} = i$,the solutions are $x = \frac{-1 \pm \sqrt{19} i}{2\sqrt{5}}$.

Solve $\sqrt{5} x^{2} + x + \sqrt{5} = 0$.

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