In the equation x^2 + kx + 54 = 0, one root is twice the other root. The value(s) of k is (are)...
(A) -5.2
(B) 15.6
(C) 22.0
(D) +- 5.2
(E) +- 15.6

Question

In the equation x^2 + kx + 54 = 0, one root is twice the other root. The value(s) of k is (are)...
(A) -5.2
(B) 15.6
(C) 22.0
(D) +- 5.2
(E) +- 15.6

albert0898 · Answer

$$x^2 + kx + 54 = 0$$

roadjester · Answer

So, you want one root to be twice the other. You'll need something along the lines of
$$(x+a)(x+2a)$$ Now foil it to get
$$x^2+3ax+2a^2=x^2+kx+54$$

albert0898 · Answer

What do I do after that?

Does that mean that 3ax = kx and that 2a^2 = 54

roadjester · Answer

Yes, and you now have a system of equations.

albert0898 · Answer

I get it now. Thank you so much! You cleared everything up for me