For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorization.


Sum of the zeroes = - 8/3


Product of the zeroes = 4/3


P(x) = x2 - (sum of the zeroes) + (product of the zeroes)


= x2 - 8x/3 + 4/3


= 3x2 - 8x + 4


By splitting the middle term


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


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