Question

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

Answer 1

As we know that the quadratic polynomial 

f(x) = k [x² - (sum of their roots) x+(product of their roots)]

According to question,

(sum of their roots)`= 2sqrt3`

And (product of their roots) = 2

Thus putting the value in above,

 `f (x) = k [x^2 - 2sqrt3x + 2 ]` where k is real number.

Therefore, the quadratic polynomial be

`f(x) = k [x^2 - 2sqrt3x + 2]`