If the roots of the equation 12x^2 - mx + 5 = | vedclass

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(A) Let the roots be $2k$ and $3k$.From the relation between roots and coefficients for the equation $12x^2 - mx + 5 = 0$:Sum of roots: $2k + 3k = \fr

Vedclass · Accepted Answer

$5\sqrt{10}$

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(A) Let the roots be $2k$ and $3k$.From the relation between roots and coefficients for the equation $12x^2 - mx + 5 = 0$:Sum of roots: $2k + 3k = \frac{m}{12}$ $\Rightarrow 5k = \frac{m}{12}$ $\Rightarrow m = 60k$ $(i)$Product of roots: $(2k)(3k) = \frac{5}{12}$ $\Rightarrow 6k^2 = \frac{5}{12}$ $\Rightarrow k^2 = \frac{5}{72}$ $\Rightarrow k = \sqrt{\frac{5}{72}} = \frac{\sqrt{5}}{6\sqrt{2}} = \frac{\sqrt{10}}{12}$.Substituting $k$ into $(i)$:$m = 60 	imes \frac{\sqrt{10}}{12} = 5\sqrt{10}$.

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$

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