Question

In the given polynomial x square - 2x - root 5, find the value of alpha - beeta

Answer 1

sum of roots ( alpha + beta ) = - b / a

=> alpha + beta = - 2/ 1..........(1)

=> alpha . beta = c / a
=> alpha. beta = -√5 / 1

=> (alpha - beta)^2 = ( alpha + beta ) ^2- 4alpha. beta

=> alpha - beta )^2 = ( -2 )^2 - 4 .(-√5)

=>( alpha - beta )^2 = 4 ( 1+ √5)

=>( alpha - beta ) = 2 √1+√5_____(2)

=> adding eq 1and 2 .....

=> 2 alpha = 2 (-1 + √1+√5)

=> alpha = --1 + √1+√5

=> beta = -2 + alpha ( from eq. 1)

=> beta = -2 -1 +√1 +√5

=> beta = -3 +√1+√5

hope this helps✌✌✌