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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