Given: One root of the equation is 5−2√5 Concept: If one root of the quadratic equation is in this form ( a+√b ) then the other roots must be conjugate ( a−√b ) and vice-versa. Quadratic equation: x2 - (sum of root) + (product of root) = 0 Calculation: Let α = 5−2√5 and β = 5+2√5 sum of root = α + β = 5−2√5+5+2√5 =10 Product of root = α β = (5−2√5)(5+2√5) = 25 - 20 = 5 Now, Quadratic equation = x2 - 10x + 5 = 0 Hence, required quadratic equation is x2 - 10x + 5 = 0