Answer:
k = -2
Step-by-step explanation:
2 way to solve:
1st: 8x²-13x-4k = 8(x²-(13/8)x-(k/2))
if 2 roots: a and 1/a
8(x-a)(x-1/a) = 8(x²-(13/8)x-(k/2))
x²-(a+1/a)x+1 = x²-(13/8)x-(k/2)
1 = -(k/2)
k = -2
2nd: 2 roots of 8x²-13x-4k x=(-b±√b²-4ac)/2a
x = (13±√169-4*8*(-4k))/16 = (13±√169+128k)/16
(13+(√169+128k))/16 = 16/ (13-(√169+128k)) ... root1=1/root2
(13+(√169+128k))*(13-(√169+128k)) = 16*16
13² - (√169+128k)² = 256
169-169-128k = 256
-128k = 256
k = -2
