Sum of the zeroes = – 8/3
Product of the zeroes = 4/3
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x)= x2 – 8x/3 + 4/3
P(x)= 3x2 – 8x + 4
Using splitting the middle term method,
3x2 – 8x + 4 = 0
3x2 – (6x + 2x) + 4 = 0
3x2 – 6x – 2x + 4 = 0
3x(x – 2) – 2(x – 2) = 0
(x – 2)(3x – 2) = 0
⇒ x = 2, 2/3