let `f(x) =px^(2)+5x+r`
since ,x-2 is a factor of f(x) , then f(2) =0
`therefore p(2)^(2)+5(2)+r=0`
`implies 4p+10+r=0`
since , `x-(1)/(2)` is a factor of f(x) , then `f((1)/(2))=0`
`therefore p((1)/(2))^(2)+5((1)/(2))+r=0`
` implies p+(1)/(4)+(5)/(2)+r=0`
`implies p+10+4r=0`
since x-2 and `x-(1)/(2) ` are factors of `f(x) =px^(2)+5x+r`
from Eqs. (i) and (ii) `4p+10+r=p+10+4rimplies 3p=3r`
`therefore p=r`
