Question

use the aleks graphing calculator to find all the zeros of the polynomial function.\\( h(x)=3x^4 + 7x^3 - 5x^2 - 12x + 3 \\)\
round to the nearest hundredth.\
if there is more than one answer, separate them with commas.\
zero(s):

Explanation:

Step1: Recall the definition of zeros

The zeros of a polynomial function \( h(x) \) are the values of \( x \) for which \( h(x) = 0 \). So we need to solve the equation \( 3x^{4}+7x^{3}-5x^{2}-12x + 3=0 \).

Step2: Use a graphing calculator (ALEKS)

We can graph the function \( y = 3x^{4}+7x^{3}-5x^{2}-12x + 3 \) and find the \( x \)-intercepts (where \( y = 0 \)). By analyzing the graph of the polynomial function, we can determine the roots.

When we graph \( h(x)=3x^{4}+7x^{3}-5x^{2}-12x + 3 \), we find the \( x \)-intercepts (zeros) by looking at where the graph crosses the \( x \)-axis. Using a graphing utility (like ALEKS), we can approximate the roots.

After using the graphing calculator, we find that the roots (rounded to the nearest hundredth) are \( x\approx - 2.72\), \( x\approx - 1.30\), \( x\approx0.27\), \( x\approx0.98\)

Answer:

-2.72, -1.30, 0.27, 0.98