Question

i want answer of example 6​

Answer 1

$here \\a = 1 \: \: b = - 5 \: c = k \\ given \: \: \alpha - \beta =1....(1) \\ \alpha + \beta = \frac{ - b}{a} \\ \: \: \: \: \: \: \: \: = \frac{5}{1} .........(2) \\ \alpha \times \beta = \frac{c}{a} = k......(3) \\ from \: eqution(1) \: and \: (2) \\ \alpha = 1 \\ \beta = 6 \\ put \: in \: (3) \\ so \:k = 6$