Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -1, 2, 3

Answer 1

f(x) = x³ - 4x² + x + 6

Explanation:

The polynomial function f has zeros at -1, 2, and 3.

So, the least degree of the polynomial will be 3{As it has three roots}.

Then, if the function is of x variable then (x + 1), (x - 2) and (x - 3) will be the factors of the polynomial.

Therefore, we can write

f(x) = (x + 1)(x - 2)(x - 3)

⇒ f(x) = (x + 1)(x² - 5x + 6)

⇒ f(x) = x³ - 5x² + 6x + x² - 5x + 6

⇒ f(x) = x³ - 4x² + x + 6

Hence, this is the polynomial with least degree having rational coefficients and with leading coefficient of 1 and the zeroes -1, 2, 3. (Answer)