Question

Find the zeros of the polynomial function j(x)=64x4+160x3+48x2−40x−16
, given its graph. Enter the zeros in order from least to greatest. Enter any non-integer numbers in decimal form.

(2 points)

Answer 1

To find the zeros of the polynomial function \( j(x) = 64x^4 + 160x^3 + 48x^2 - 40x - 16 \), we can factor the polynomial or use numerical methods (like the Rational Root Theorem) or graphing tools to look for potential roots.

In this case, let's start by factoring or using synthetic division. However, given the complexity of the polynomial, numerical methods or graphing software might be more effective.

Upon graphing or calculating, we find that the zeros are approximately:

1. \( x \approx -2 \)
2. \( x \approx -0.5 \)
3. \( x \approx 0.25 \)
4. \( x \approx 0.5 \)

Arranging these in order from least to greatest:

1. \( -2 \)
2. \( -0.5 \)
3. \( 0.25 \)
4. \( 0.5 \)

Thus, the zeros of the polynomial function \( j(x) \) are:
\[-2, -0.5, 0.25, 0.5\]