Question

53. If the roots of the equation 3x2 + 9x + 2 = 0 are in
the ratio m:n, then find
root (m/n)+root (n/m)​

Answer 1

SOLUTION

GIVEN

The roots of the equation 3x² + 9x + 2 = 0 are in the ratio m : n

TO DETERMINE

The value of

EVALUATION

Here it is given that the roots of the equation 3x² + 9x + 2 = 0 are in the ratio m : n

Let the roots are mk and nk

Then mk + nk = - 3

$\displaystyle \sf{mk \times nk = \frac{2}{3} }$

Now

$\displaystyle \sf{ \sqrt{ \frac{m}{n} } + \sqrt{ \frac{n}{m} } }$

$\displaystyle \sf{ = \frac{m + n}{ \sqrt{mn} } }$

$\displaystyle \sf{ = \frac{mk + nk}{k \sqrt{mn} } }$

$\displaystyle \sf{ = \frac{mk + nk}{ \sqrt{mk \times nk} } }$

$\displaystyle \sf{ = \frac{ - 3}{ \sqrt{ \frac{2}{3} } } }$

$\displaystyle \sf{ = \frac{ - 3 \sqrt{3} }{ \sqrt{2} } }$

$\displaystyle \sf{ = - \frac{ 3 \sqrt{6} }{ 2 } }$

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Answer 2

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