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 = 0

∴ ab = c/a = √5

If a = k, where k is any real number,

b = 0 ………………… (ii)

c = √5k ………………… (iii)

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

kx² + (0)x + (√5k) = 0

k (x² + √5) = 0

Therefore the quadratic equation is as follows:

x² + √5 = 0