Question

the roots alpha and beta of a polynomial x^2-5x+3(k-1)=0 are such that alpha-beta =1 then find the value of K​

Answer 1

$\huge\bold{\mathtt{\purple{A {\pink {N {\green {S{\blue{W {\red{E {\orange {R}}}}}}}}}}}}} \\ \bf \: \alpha + \beta = 5......(1) \\ \bf \: \alpha - \beta = 1......(2) \\ \bf \: solving \: (1) \: and \: (2).we \: get \\ \bf \: \alpha = 3 \: and \: \beta = 2 \\ \bf \: also \: \alpha \beta = 6 \\ \bf \: or \: 3(k - 1) = 6 \\ \bf k - 1 = 2 \\ \bf \: k = 3$