The correct answer is (b) √3
To explain: α and β are the zeros of x^2 – (5 + 7k)x + 35k
So, α + β = (5 + 7k) and αβ = 35k
Also, α^2 + β^2 = 172
(α + β)^2 – 2αβ = 172
Substituting values we get,
(5 + 7k)^2 – 2(35k) = 172
25 + 49k^2 + 70k – 70k = 172
49k^2 – 147 = 0
Solving we get, k = √3