Question

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

Answer 1

$f(x) = px {}^{2} + 5x + r \\ given \: that \:( x - 2) \: and(x - \frac{1}{2} )are \: factors \\ then \: (x - 2)( x - \frac{1}{2} ) = px {}^{2} + 5x + r \\ (x - 2)(2x - 1) = px {}^{2} + 5x + r \\ 2 {x}^{2} - 5x + 2 = px {}^{2} + 5x + r \\ so \: p = 2 \: and \: r = 2$
hence p=2 and r=2
here is your answer