Question

For 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 factorisation.

`-2sqrt(3), -9`

Answer 1

Sum of the zeroes = `- 2sqrt(3)`

Product of the zeroes = – 9

P(x) = x² – (Sum of the zeroes) + (Product of the zeroes)

Then, P(x) = `x^2 - (-2sqrt(3)x) - 9`

Using splitting the middle term method,

`x^2 + 2sqrt(3)x - 9` = 0

`x^2 + (3sqrt(3)x - sqrt(3)x) - 9` = 0

`x(x + 3sqrt(3)) - sqrt(3)(x + 3sqrt(3))` = 0

`(x - sqrt(3))(x + 3sqrt(3))` = 0

`\implies` x = `sqrt(3), -3sqrt(3)`