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.

- 23, - 9

Sum of the zeroes = - 2√3

Product of the zeroes = - 9

P(x) = x^{2} - (sum of the zeroes) + (product of the zeroes)

= x^{2} - 2√3x 9

By splitting the middle term

x^{2} - 2√3x - 9 = 0

x^{2} - (- √3x + 3√3x) - 9 = 0

x^{2} + √3x - 3√3x - 9 = 0

x(x + √3) - 3√3(x + √3) = 0

(x + √3)(x - 3√3) = 0

⇒ x = - √3, 3√3

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