Solution:

From the given polynomial p(x),

α + β **= −4/r**, and αβ = **−4/r**………. (1)

Since,**(α + β)**^{2} = α^{2} + β^{2} + 2αβ

Given, **α**^{2} + β^{2} = 24 and from **equation (1).**

Therefore, (−4/r)^{2}=24+(2×4)/r

16/r^{2}=24+(2×4)/r

16 = 24 r^{2} + 8r

3r^{2} + r – 2 = 0

3r^{2} + 3r – 2r -2 = 0

3r(r+1) – 2(r+1) = 0

(3r-2) (r+1) = 0

**∴ r = 2/3** or **r = -1**