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 = 21/8
Product of the zeroes = 5/16
P(x) = x2 - (sum of the zeroes) + (product of the zeroes)
= x2 - 21x/8 + 5/16
= 16x2 - 42x + 5
By splitting the middle term
16x2 - 42x + 5 = 0
16x2 - (2x + 40x) + 5 = 0
16x2 - 2x - 40x + 5 = 0
2x (8x - 1) - 5(8x - 1) = 0
(8x - 1)(2x - 5) = 0
⇒ x = 1/8, 5/2
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