Respuesta :
Answer:
k=1/4
Step-by-step explanation:
x² - 5kx+ k=0 ....(1)
suppose 2 roots: a and 4a
(x-a)(x-4a)=0
x² - 5ax + 4a² = 0 ....(2)
compare (1) and (2): -5a = -5k a=k
4a² = k 4a² = a (substitute)
a(4a-1) = 0
a = 0 or a = 1/4 (if a=0 k=0 and x=0 is not the solution)
a = 1/4 k = 1/4
(a₂ = 1/4 * 4 = 1)
Answer:
k = 1/4.
Step-by-step explanation:
Let the roots be r and 4r and using the fact that sum of the roots = -b/a and product = a/c, we have:
r + 4r = -(-5k)
r*4r = k
5r = 5k
4r^2 = k
From the 3rd equation:
r = k, therefore:
4k^2 = k
4k = 1
k = 1/4.
