Question

Find the value of m if the roots of the equation y^ 2+ my + 12 = 0 are in the ratio 1/3​

Answer 1

SOLUTION

TO DETERMINE

The value of m if the roots of the equation

$\sf{ {y}^{2} + my + 12 = 0 \: are \: in \: the \: ratio \: 1 : 3}$

EVALUATION

Here the given equation is

$\sf{ {y}^{2} + my + 12 = 0}$

It is given that the roots are in the ratio 1 : 3

Let roots are k and 3k

Sum of the roots = k + 3k = 4k

Product of the roots

$= \sf{k \times 3k}$

$= \sf{3 {k}^{2} }$

Also from the given equation

Sum of the roots = - m

Product of the roots = 12

$\sf{ \implies \: 3 {k}^{2} = 12 }$

$\sf{ \implies \: {k}^{2} = 4}$

$\sf{ \implies \: k = \pm \: 2}$

Again

$\sf{m = - 4k}$

$\implies \sf{m = \pm \: 8}$

Hence the required value of m is

$\sf{ \pm \: 8}$

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