Question

Write a polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form for the zeros: 3, 4+2i, 1+√7.

a) x^4 - 8x^3 + 29x^2 - 48x + 24
b) x^3 - 8x^2 + 24x - 24
c) x^3 - 4x^2 - 3x + 2√7
d) x^4 - 9x^3 + 29x^2 - 24x + √7

Answer 1

The polynomial function of least degree with rational coefficients, a leading coefficient of 1, and the given zeros is x^4 - 9x^3 + 29x^2 - 24x + √7.Correct option is a.

Step-by-step explanation:

To write a polynomial function of least degree with rational coefficients and a leading coefficient of 1, we can use the zeros given. The zeros are 3, 4+2i, and 1+√7.

Since the zeros come in pairs (4+2i and 4-2i), we know that the imaginary parts cancel out and we are left with real zeros 3, 4, and 1+√7.

The polynomial function in standard form using these zeros is (x-3)(x-4)(x-(1+√7))(x-(1-√7)).

Simplifying this expression gives us the polynomial function: x^4 - 9x^3 + 29x^2 - 24x + √7.