The roots of the equation sqrt{7} x^{2}-6 x-1 | vedclass

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Question

(C) Given equation: $\sqrt{7} x^{2}-6 x-13 \sqrt{7}=0$To solve by splitting the middle term,we need two numbers whose product is $(\sqrt{7}) 	imes (-

Vedclass · Accepted Answer

$-\sqrt{7}, \frac{13 \sqrt{7}}{7}$

Vedclass · Answer

(C) Given equation: $\sqrt{7} x^{2}-6 x-13 \sqrt{7}=0$To solve by splitting the middle term,we need two numbers whose product is $(\sqrt{7}) 	imes (-13 \sqrt{7}) = -91$ and whose sum is $-6$.These numbers are $-13$ and $7$.$\sqrt{7} x^{2}-13 x+7 x-13 \sqrt{7}=0$Taking common terms:$x(\sqrt{7} x-13)+\sqrt{7}(\sqrt{7} x-13)=0$$(x+\sqrt{7})(\sqrt{7} x-13)=0$Setting each factor to zero:$x+\sqrt{7}=0 \Rightarrow x=-\sqrt{7}$$\sqrt{7} x-13=0 \Rightarrow x=\frac{13}{\sqrt{7}} = \frac{13 \sqrt{7}}{7}$Thus,the roots are $-\sqrt{7}$ and $\frac{13 \sqrt{7}}{7}$.

The roots of the equation $\sqrt{7} x^{2}-6 x-13 \sqrt{7}=0$ are

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