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The nonzero roots of the equation $x^2 + 6x + k = 0$  are in the ratio $2:1$ . What is the value of $k$ ?

 Jan 2, 2021
 #1
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Let the roots be r and 2r:

 

(x-r)*(x-2r) = x^2 + 6x + k

 

x^2 - 3rx + 2r^2 =  x^2 + 6x + k

 

Compare coefficients

-3r = 6,  hence r = -2

 

k = 2r^2  Hence k = 8

 Jan 2, 2021

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