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 = 
Product of the zeroes = - 1/2
P(x) = x2 - (sum of the zeroes) + (product of the zeroes)
= x2 - 
x - 1/2
= 2√5x2 - 3x - √5
By splitting the middle term
2√5x2 - 3x - √5 = 0
2√5x2 - (5x - 2x) - √5 = 0
2√5x2 - 5x + 2x - √5 = 0
√5x (2x - √5) - (2x - √5) = 0
(2x - √5)(√5 - 1) = 0
⇒ x = - 1/√5, √5/2
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