Question

1-29

In the equation x² + 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

Answer 1

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