Answer :

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


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