Sum of the zeroes = -3/2√5x
Product of the zeroes = – ½
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x)= x2 -3/2√5x – ½
P(x)= 2√5x2 – 3x – √5
Using splitting the middle term method,
2√5x2 – 3x – √5 = 0
2√5x2 – (5x – 2x) – √5 = 0
2√5x2 – 5x + 2x – √5 = 0
√5x (2x – √5) – (2x – √5) = 0
(2x – √5)(√5 – 1) = 0
⇒ x = – 1/√5, √5/2