Question

If one of the roots of the equation x²- 4x + k=0exceeds the other by 2, then find the roots and determine the value of k

Answer 1

roots: 1 and 3

k = 3

Explanation:

2 roots: p and p+2

(x-p) (x-p-2) = x² - 4x + k

x² -2px -2x + p² + 2p = x² - 2 (p+1)x + (p² + 2p) = x² -4x + k

-2 (p+1) = -4

p+1 = 2

p = 1 ... root 1

p' = 1+2 = 3 ... root 2

k = p² + 2p = 3

check: (x-1) (x-3) = x² - 4x + 3 = x² - 4x + k