Question

The equation 3x2 + mx + n = 0 has roots that are double that of the equation x2 + 10x + 12 = 0. What is the value of m + n?

Answer 1

Let α be the roots of $x^{2} -x + m=0$ and 2a be the root of $x^{2} -3x+2m = 0$

Then, $a^{2} -a+m=0$

and $4a^{2} -6a +2m=0$

On solving these equations, we get

$\frac{a^{2} }{-2m+6m} = \frac{a}{4m-2m} = \frac{1}{-6+4}$

$\frac{a^{2} }{4m} = \frac{a}{2m} = \frac{1}{-2}$

$a^{2} =-2m$ and $a=-m$

∴ $(-m^{2})=-2m$

$m^{2} +2m=0$

$m(m+2)=0$

∴ $m=0,m=-2$

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