Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. √(2 ) ,1/3

Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = √2 = (3√2)/3 = (-b)/a
αβ = 1/3 = c/a
On comparing,
a = 3, b =-3/√2 and c = 1
Hence, the required quadratic polynomial is 3x² – 3/√2 + 1.

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Understanding polynomials is essential for further study in mathematics, including topics such as algebra and calculus. Studying polynomials helps students develop important mathematical skills, such as algebraic manipulation, problem-solving, and critical thinking.