Given that one root of the quadratic equation is √5 + √2.
∴ Other root of the quadratic equation is √5 - √2.
∴ Required quadratic equation is (x - (√5 + √2)) (x - (√5 - √2)) = 0
⇒ ((x - √5) - √2) ((x - √5) + √2) = 0
⇒ (x - √5)2 - 2 = 0 (∵ (a-b) (a+b) = a2 - b2)
⇒ x2 - 2√5x + 5 - 2 = 0 (∵ (a - b)2 = a2 - 2ab + b2)
⇒ x2 - 2√5x + 3 = 0
