Find a quadratic

Let the two zeroes be a and b.

The generalized form of the quadratic equation with sum and product of zeroes a and b is as follows:

ax² + bx + c = 0 ………………… (i)

Now in this case

∴ a + b = -b/a = √2

∴ ab = c/a = 1/3

If a = k, where k is any real number

b = -√2k ………………… (ii)

c = k/3 ………………… (iii)

Put values from (ii) and (iii) in (i)

kx² - √2kx + k/3 = 0

3kx² - 3√2kx + k = 0

k (x² - 3√2x + 1) = 0

Therefore the quadratic equation is as follows:

(x² - 3√2x + 1) = 0