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In the equation x² + kx + 54=0, one root is twice the other root. The value(s) of k is (are)

A-5.2
B15.6
C22.0
D± 5.2
E± 15.6

Verified Answer :

konrad509

\(x_1+x_2=-\dfrac{b}{a}=-k\\ x_1x_2=\dfrac{c}{a}=54\\ x_1=2x_2\\\\ 2x_2+x_2=-k\\ 3x_2=-k\\ x_2=-\dfrac{k}{3}\\\\ 2x_2\cdot x_2=54\\ 2x_2^2=54\\ x_2^2=27\\\\ \left(-\dfrac{k}{3}\right)^2=27\\ \dfrac{k^2}{9}=27\\ k^2=243\\ k=\pm\sqrt{243}\\ k\approx\pm15.6\)

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