Question

One root of the equation x^2+kx+2k=0 (k!=0) is twice the other. Find k and find the roots of the equation.

Answer 1

yeah...

Answer 2

haha

Answer 3

(k!=0) isn't the only way this is possible is to have k=0?

Answer 4

have you tried systems of equations?
eq 1: k!=0
eq 2: x_1 = 2x_2
eq 3: x_1,x_2 = quadratic equation

Answer 5

I got k = 9 with x=-3, -6
does that sound correct?

Answer 6

It sounds correct, but I have no idea how you did it.

Answer 7

First use the quadratic equation, and turn it into two equations becuase there are two roots, so the + and - part is where you split it into two equations. then set one equation equal to x_1 and the other equation equal to x_2.
and recall that "twice the other" is one root to the first, so then I used x_1 = 2x_2
which eliminates the x_1 of the quatric eq and turns it into 2x_2. so now I have my two quatratic equations, but they now both equal x_2.
set them equal to each other, solve for k.
once you get k, plug k back into the original equation, use the quadrtic eq again to solve for x.

Answer 8

I don't get it O_o
Are x_1 and x_2 variables?

Answer 9

yaya, x'sub'1 and x'sub'2