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


1