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Find the quadratic polynomial, whose zeroes are 2/3 and 2.

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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.

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