Question

if both x-2 and x-1/2 are factors of PX^2+5x+r , then the relation between p and r , is​

Answer 1

Question:-

if both x-2 and x-1/2 are factors of PX^2+5x+r , then the relation between p and r , is

Answer:-

$\star \bf{\: x - 2 = 0} \\ \bf{x = 2} \\ \red{ \bf{and }}\\ \star \bf{ \: x - \frac{1}{2} = 0 }\\ \bf{ x = \frac{1}{2} } \\ \\ (1) \: \bf{if \: x = 2} \\ \\ \implies \bf{ \: p {x}^{2} + 5x + r} \\ \\ \implies \: \bf{4p + 10 + r} \\ \\ (2) \: \bf{if \: x = \frac{1}{2} } \\ \\ \implies \: \bf{ \: p {x}^{2} + 5x + r} \: \\ \\ \implies \: \bf{ \frac{p}{4} + \frac{5}{2} + r}$