High School

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Find the zeros of the function:

[tex] F(x) = 25x^3 - 8 [/tex]

Answer :

To find the zeros of the function [tex]\( F(x) = 25x^3 - 8 \)[/tex], follow these steps:

1. Set the Function Equal to Zero:
[tex]\[
25x^3 - 8 = 0
\][/tex]

2. Isolate the Cubic Term:
Add 8 to both sides of the equation to isolate the term with [tex]\( x^3 \)[/tex]:
[tex]\[
25x^3 = 8
\][/tex]

3. Solve for [tex]\( x^3 \)[/tex]:
Divide both sides by 25 to solve for [tex]\( x^3 \)[/tex]:
[tex]\[
x^3 = \frac{8}{25}
\][/tex]

4. Take the Cube Root:
To find [tex]\( x \)[/tex], take the cube root of both sides:
[tex]\[
x = \sqrt[3]{\frac{8}{25}}
\][/tex]

Calculating the cube root of [tex]\(\frac{8}{25}\)[/tex], we get:

[tex]\[
x \approx 0.6839903786706788
\][/tex]

Therefore, the zero of the function [tex]\( F(x) = 25x^3 - 8 \)[/tex] is approximately [tex]\( x = 0.6839903786706788 \)[/tex].

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