Find the quadratic polynomial, the sum of whose roots is √2 and their product is 1/3.

Let the zero of the polynomial be α and β

According to the question,


α + β = √2



f(x)= x2 – (α + β)x + (αβ)



required polynomial f(x)= x2 - √2 x + 1/3


Put f(x) = 0


x2 - √2 x + 1/3 = 0


3x2 – 3√2x + 1 = 0


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