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
2