78.7k views
1 vote
In the equation x^2+kx+54=0 one root is twice the other root find k

1 Answer

1 vote
Let r be the lesser root and r^2 be the greater.......the sum of the roots = -b/a = -[-6] / 1 = 6



So we have that



r^2 + r = 6 → r^2 + r - 6 = 0



Factor



(r + 3) (r - 2) = 0



So r = -3 or r = 2



Then r^2 = 9 or r^2 =4



And the product of the roots = c/a = k/a = k



So....k = (-3)(9) = -27 or k = (2)(4) = 8



Check



x^2 - 6x - 27 = 0 factors as (x + 3)(x - 9) = 0 and the roots are -3 and 9



x^2 - 6x + 8 = 0 factors as (x -2) (x - 4) =0 and the roots are 2 and 4



User Kpblc
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories