Solution:
From the given polynomial p(x),
α + β = −4/r, and αβ = −4/r………. (1)
Since,(α + β)2 = α2 + β2 + 2αβ
Given, α2 + β2 = 24 and from equation (1).
Therefore, (−4/r)2=24+(2×4)/r
16/r2=24+(2×4)/r
16 = 24 r2 + 8r
3r2 + r – 2 = 0
3r2 + 3r – 2r -2 = 0
3r(r+1) – 2(r+1) = 0
(3r-2) (r+1) = 0
∴ r = 2/3 or r = -1
