Question

i do not understand the first question's solution.

50f31eef64c9b279efce4ce1e23282e4.pdf

Answer 1

Assuming root 'a'
Therefore, second root = 6a
Both satisfy equation kx^2-14x+8 = 0

1. Substituting root 'a' into equation:
=> ka^2-14a+8 = 0 ...(1)
=> 9ka^2-126a+72 = 0 (Multiplying equation with 9) ...(2)

2. Substituting root 6a into the equation:
=> 36ka^2-84a+8 = 0
=> 9ka^2-21a+2 = 0 (Dividing equation by 4) ...(3)
Subtracting equations (3) from (2), we get
=> -105a+70 = 0
=> a = 70/105 = 2/3

Substituting root 'a' in equation (1)
=> 4k/9-28/3+8 = 0
=> (4k-84+72)/9 = 0
=> 4k-12 = 0
=> 4k = 12
=> k = 3

Alternate Method, which is too much effort to type out: