Question

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots sqrt 5 and 2

Answer 1

f(x) = 3x² -21x + 30

Explanation:

Polynomial function of lowest degree with roots as 'a' and 'b' and leading coefficient as 'c' is given by:

P(x) = c (x - a) (x - b)

Given: Leading coefficient = 3, Roots = sqrt 5 and 2

P(x) = 3 (x - 5) (x - 2)

= 3 ( x² - 2x - 5x +10)

= 3 ( x² - 7x +10)

= 3x² - 21x + 30