Let `alpha` and `beta` be the given roots of a quadratic equation, then

`(x - alpha) (x - beta) = 0`

`x^2 - x (alpha + beta) + alphabeta = 0`

`x^2 - x (`sum of the roots`) +` Product of the roots`= 0`

`text(Note :)` Some Transformation in terms `alpha + beta` and `alphabeta`


`alpha ^2 +beta^2 = (alpha +beta)^2 - 2alphabeta`

`alpha^3 + beta^3 = (alpha+ beta)^3 - 3alphabeta(alpha + beta)`

`alpha -beta = sqrt((alpha + beta) ^2 - 4alphabeta)`

`alpha^4 + beta^4 = [(alpha + beta)^2 - 2alphabeta]^2 - 2alpha^2beta^2`