Let f(x)= px² +5x +r

Since, x-2 and x-1/2 are factors of f (x)

f (2) = 0

4p + 10 + r = 0 (i)

f(1/2) = 0

p + 10 + 4r = 0 (ii)

(i) * (ii), we get,

4p + 40 + 16r = 0 (iii)

Subtracting (i) and (iii)

-30 - 15r = 0

r = - 2

Putting value of r in (i),

4p + 10 - 2 = 0

p = -2

Therefore, p = r