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Question
Write a quadratic polynomial, sum of whose zeros is \[2\sqrt{3}\] and their product is 2.
Solution
Let S and P denotes respectively the sum and product of the zeros of a polynomial are `2sqrt3` and 2.
The required polynomial g(x) is given by
`g(x) = k (x62 - Sx + p)`
`g(x)= k (x ^2 - 2sqrt3 + 2)`
Hence, the quadratic polynomial is `g(x) = k (x^2 - 2sqrt3x + 2)` where k is any non-zeros real number.
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