Let the quadratic polynomial be ax2 + bx + c, a ≠ 0 and its zeroes be α and β.
Here α = \(\frac{2}{3}\) and β = 2.
Sum of the zeores = α + β = \(\frac{2}{3}\) + 2 = \(\frac{8}{3}\)
Product of the zeroes = αβ = \(\frac{2}{3}\) (2) = \(\frac{4}{3}\)
∴ The quadratic polynomial
ax2 + bx + c is = [x2 – (α + β)x + αβ]
= [x2 – \(\frac{8}{3}\)x + \(\frac{4}{3}\) ]
The quadratic polynomial will be 3x2 – 8x + 4.