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Mathematics

Solve the following equation using the formula :

6x2−4x−26=0\sqrt{6}x^2 - 4x - 2\sqrt{6} = 0

Quadratic Equations

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Answer

Comparing 6x2−4x−26=0\sqrt{6}x^2 - 4x - 2\sqrt{6} = 0 with ax2 + bx + c = 0 we get,

a=6,b=−4,c=−26.a = \sqrt{6}, b = -4, c = -2\sqrt{6}.

We know that,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get,

⇒x=−(−4)±(−4)2−4(6)(−26)26=4±16+4826=4±6426=4±826=4+826 or 4−826=1226 or −426=6 or −26=2.45 or −26=2.45 or −26×66=2.45 or −266=2.45 or −63=−0.82\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(\sqrt{6})(-2\sqrt{6})}}{2\sqrt{6}} \\[1em] = \dfrac{4 \pm \sqrt{16 + 48}}{2\sqrt{6}} \\[1em] = \dfrac{4 \pm \sqrt{64}}{2\sqrt{6}} \\[1em] = \dfrac{4 \pm 8}{2\sqrt{6}} \\[1em] = \dfrac{4 + 8}{2\sqrt{6}} \text{ or } \dfrac{4 - 8}{2\sqrt{6}} \\[1em] = \dfrac{12}{2\sqrt{6}} \text{ or } \dfrac{-4}{2\sqrt{6}} \\[1em] = \sqrt{6} \text{ or } -\dfrac{2}{\sqrt{6}} \\[1em] = 2.45 \text{ or } -\dfrac{2}{\sqrt{6}} \\[1em] = 2.45\text{ or } -\dfrac{2}{\sqrt{6}} \times \dfrac{\sqrt{6}}{\sqrt{6}} \\[1em] = 2.45 \text{ or } -\dfrac{2\sqrt{6}}{6} \\[1em] = 2.45 \text{ or } -\dfrac{\sqrt{6}}{3} = -0.82

Hence, x = 2.45, -0.82.

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