Question

Find the zeros of the polynomial below j(x) = 12^3/5 - 27x/5

Answer 1

To find the zeros of the polynomial \( j(x) = \frac{12^3}{5} - \frac{27x}{5} \), we can set the polynomial equal to zero and solve for \( x \).

Starting with the equation:

\[
\frac{12^3}{5} - \frac{27x}{5} = 0
\]

We can eliminate the fraction by multiplying through by 5:

\[
12^3 - 27x = 0
\]

Next, solve for \( x \):

\[
27x = 12^3
\]

Now calculate \( 12^3 \):

\[
12^3 = 12 \cdot 12 \cdot 12 = 144 \cdot 12 = 1728
\]

So we have:

\[
27x = 1728
\]

Now, divide both sides by 27 to isolate \( x \):

\[
x = \frac{1728}{27}
\]

Now perform the division:

\[
\frac{1728}{27} = 64 \quad \text{(since \( 27 \times 64 = 1728 \))}
\]

Thus, the zero of the polynomial \( j(x) \) is:

\[
x = 64
\]