Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

`sqrt2 , 1/3`

Answer 1

`sqrt2, 1/3`

Let the polynomial be ax² + bx + c, and its zeroes be α and ß

Given α + ß = `sqrt2` = `(-b)/a`

αß = `1/3 = c/a`

If a = 3, then b = `sqrt2` and  c = 1/3

Therefore, the quadratic polynomial is 3x² - `3sqrt2` x +1.