Quadratic equation corresponding to the roots 2 + √5 and 2 - √5 is-

Question: Quadratic equation corresponding to the roots 2 + √5 and 2 - √5 is-

Solution:
The quadratic equation is: x² - (Sum of roots)x + Product of roots = 0

Let the roots of the equation be A and B.
A = 2 + √5 and B = 2 - √5

∴ A + B = 2 + √5 + 2 - √5 = 4

∴ A × B = (2 + √5)(2 - √5) = 4 - 5 = - 1

Then equation is
x² - 4x - 1 = 0