Question

Find a quadratic polynomial, the sum and product of whose zeroes are -2√3 and -9, respectively. Also find its zeroes.

Answer 1

Sum of the zeroes = – 2√3

Product of the zeroes = – 9

P(x) = x² – (sum of the zeroes) + (product of the zeroes)

Then, P(x) = x² – 2√3x- 9

Using splitting the middle term method,

x² – 2√3x – 9 = 0

x² – (- √3x + 3√3x) – 9 = 0

x² + √3x – 3√3x – 9 = 0

x(x + √3) – 3√3(x + √3) = 0

(x + √3)(x – 3√3) = 0

⇒ x = – √3, 3√3