Construct a quadratic equation whose roots are √2 and 2 √2

Let k₁ and k₂ be the roots of quadratic equation .
Given :- k₁ = √2 and k₂ = 2 √2
Sum of the roots = √2 + 2 √2 = 3 √2
Product of the roots = ( √2 ) ( 2√2 ) = 4
Hence the required quadratic equation is x ² = (sum of the roots) x + (Product of two roots) = 0
⇒ x ² - 3 √2x + 4 = 0.