The nonzero roots of the equation x^2 + 6k + x = 0 are in the ratio 2:7 . What is the value of k?
Let one root = a and the other be (7/2)a
By Vieta :
a + (7/2)a = -1
(9/2)a = -1
a = -1/(9/2) = -2/9
(7/2)a = (7/2)(-2/9) = -7/9
Also, byVieta :
a * (7/2)a = k
(-2/9) (-7/9) = k = 14/81
