Question

find the quadratic equation with the roots 2+√5 and 2-√5

Answer 1

roots = 2 + √5 , 2 - √5

Sum of roots = 2 + √5 + 2 - √5 = 4
Product of roots = (2 +√5)(2 - √5) = 2² - (√5)² = 4 - 5 = -1

Quadratic equation = k [ x² - (sum of roots)x + (product of roots) ]
                                  = k [x² - 4x - 1]
                                  = x² - 4x - 1 (where k = constant)

Hope This Helps You!

Answer 2

(x-2-√5)(x+2+√5)
=(x-2)(x+2+√5)-√5(x+2+√5)