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If both x-2 and x-1/2 are factors of p x...

If both `x-2` and `x-1/2` are factors of `p x^2+5x+r ,` show that `p=rdot`

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`x-2`is a factor of `p x^2+5x+r`
`x-2=0,x=2,p(2)^2+5(2)+r=0`
`4p+10+r=0`
`4p+r=-10(i)`
`x=1/2,p(1/2)^2+5(1/2)+r=0`
`p/4+5/2+r=0`
`(p+10+4r)/4=0`
`p+4r=-10 (ii)`
comparing `(i) \and\(ii),p=r`
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