Answer:
k = 15, m = 3
Explanation:
Since 2 and m are roots of the equation, then substituting x = 2 and x = m into the equation makes it true
x = 2 : (3)(5) = k(1) ⇒ k = 15
x = m : (2m - 1)(m + 3) = 15(m - 1) ← expand factors on both sides
2m² + 6m - m - 3 = 15m - 15
rearrange into standard form
2m² - 10m + 12 = 0 ← in standard form
divide all terms by 2
m² - 5m + 6 = 0
(m - 2)(m - 3) = 0 ← in factored form
equate each factor to zero and solve for m
m - 2 = 0 ⇒ m = 2
m - 3 = 0 ⇒ m = 3
We know x = 2 is a root, hence m = 3
The roots are x = 2, x = 3 and k = 15