Explanation

Given:

α + β = 5 (sum of roots)

αβ = k (product of roots)

3α + 2β = 16

From α + β = 5, we get:

α = 5 - β

Substitute α in 3α + 2β = 16:

3(5 - β) + 2β = 16

15 - 3β + 2β = 16

-β = 1

β = -1

Now, α = 5 - β

α = 5 - (-1)

α = 6

k = αβ

k = 6 × (-1)

k = -6