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.

Question

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. - 2 3, - 9

Philoid · Accepted Answer

Sum of the zeroes = - 2√3

Product of the zeroes = - 9

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

= x² - 2√3x 9

By splitting the middle term

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

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

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