Question

If one zero of the following polynomial 8x^2-13x-4k is the reciprocal of the other, then find k

Answer 1

k = -2

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