Question

Write a quadratic polynomial, sum of whose zeros is \[2\sqrt{3}\] and their product is 2.

Answer 1

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 (x^2 - 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.