Questions: Question 3 5 pts Find the zeros of f(x), given that one zero is k. f(x) = x^4 - 6x^3 + 3x^2 + 24x - 28 k=2 ±2, -3 ± 2i ±2, 3 ± √2 ±2, 3 ± 2i ±2, -3 ± √2 i

Solution Steps

To find the zeros of the polynomial \( f(x) = x^4 - 6x^3 + 3x^2 + 24x - 28 \) given that one zero is \( k = 2 \), we can use polynomial division to factor out \( (x - 2) \) from \( f(x) \). After factoring, we solve the resulting polynomial equation to find the remaining zeros.

We are given the polynomial \( f(x) = x^4 - 6x^3 + 3x^2 + 24x - 28 \) and know that one of its zeros is \( k = 2 \).

Using polynomial division, we factor out \( (x - 2) \) from \( f(x) \). This results in a cubic polynomial, which we can denote as \( g(x) \).

After factoring, we find the zeros of the cubic polynomial \( g(x) \). The zeros of the original polynomial \( f(x) \) are the solutions to \( g(x) = 0 \) along with the known zero \( k = 2 \).

From the calculations, the zeros of \( f(x) \) are approximately:

• \( 4.4142 \)
• \( -2 \)
• \( 2 \)
• \( 1.5858 \)

Final Answer