The quadratic equation with rational coefficients, whose one root is √5, is :

As per the given above question , we have
Let k₁ and k₂ be the roots of quadratic equation .
One root is k₁ = √5
So the other root is k₂ = − √5
∴ Sum of the roots = k₁ + k₂ = √5 + ( -√5 ) = 0
and product of the roots = k₁ × k₂ = − (√5) (- √5) = −5
∴ Required equation is x² - (sum of the roots)x + (product of the roots) = 0
⇒ x² - 5 = 0.