roots
Algebra
Level
3
r is a root of x^2 + kx = -6
and
r+5 is a root of -3x^2 + 3kx = 18
find the value of k
The answer is 5.
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1 solution
If r is the solution, then r^2 + kr + 6 = 0. If r+5 is the solution of x^2 - kx +6 = 0, then (r+5)^2 - (r+5)k +6 = 0, 0r r^2 + 10r+25 -kr-5k + 6 = 0, this can be simplified to (-2k+10)r +(25 - 5k) = 0, then k=5.