Question

For what value of n, the ratio of the roots of x²-5x+(n+1)=0 is 2:1 ?
a) 2
b) 3
c) ½
d) 5

Answer 1

$let \: the \: roots \: be \: \alpha \: and \: \beta \\ given \: \frac{ \alpha }{ \beta } = 2 \\ from \: the \: equation \\ \alpha + \beta = 5 \\ 2 \beta + \beta = 5 \\ \beta = \frac{5}{3} . \: therefore \: \alpha = 2 \times \frac{5}{3} = \frac{10}{3} \\ from \: equation \: \: \alpha \beta = n + 1 \\n = \alpha \beta - 1 = \frac{50}{9} - 1 = \frac{41}{9}$