Question

Find the zeros of the function f(x) = x⁴ + 5x³ - 7x² - 29x + 30.

a) -3 and 2
b) -2 and 3
c) 1 and -5
d) 4 and -1

Answer 1

The zeros of the polynomial function f(x) = x⁴ + 5x³ - 7x² - 29x + 30 are found by testing the given options; -3 and 2 are both zeros of the function, corresponding to option a).

Step-by-step explanation:

The student has asked to find the zeros of the function f(x) = x⁴ + 5x³ - 7x² - 29x + 30. To find the zeros of the polynomial, we can try to factor the polynomial or use methods such as synthetic division or the Rational Root Theorem to find potential rational zeros. However, for this multiple-choice question, we can test the provided options to see which ones are indeed zeros of the polynomial.

Let us substitute each option into the polynomial:

Since both -3 and 2 result in the function equating to zero, options b), c), and d) need not be checked. We have found that the zeros of the function are -3 and 2, which corresponds to option a).