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Question

Find a quadratic polynomial with the given number as the sum and the product of its zeroes respectively

√2 , 1/3

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Solution

A quadratic equation is given by

x²-(sum of roots)x+(product of roots) = 0
​​​​​​
here given,
Sum of roots = √2
Product of roots = 1/3

So equation become
​​​​​​ x²-√2x+(1/3) = 0

Multiply with 3 to remove denominator

3x²-3√2x+1 = 0 , the required equation

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