High School

Find all the zeros of the equation:

\[ x^5 - 3x^4 - 15x^3 + 45x^2 - 16x + 48 = 0 \]

Answer :

Final answer:

To find the zeros of the equation x^5 - 3x^4 - 15x^3 + 45x^2 - 16x + 48 = 0, we need to factor the polynomial. By using polynomial long division or synthetic division, we can determine that x = -1 is a zero of the polynomial.

Explanation:

To find the zeros of the equation x^5 - 3x^4 - 15x^3 + 45x^2 - 16x + 48 = 0, we need to factor the polynomial.

By using polynomial long division or synthetic division, we can determine that x = -1 is a zero of the polynomial. Dividing the polynomial by (x + 1), we find a quotient of x^4 - 4x^3 - 11x^2 + 34x - 48.

Using a graphing calculator or factoring techniques, we can further factor the quartic polynomial and find the remaining zeros.

Learn more about Finding zeros of a polynomial here:

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