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Answer :
Sure, I'd be happy to help with finding the zero of the function [tex]\( f(x) = 27x^3 - 27x^2 + 9x - 1 \)[/tex]. Here's the step-by-step solution:
To find the zeros of the function [tex]\( f(x) = 27x^3 - 27x^2 + 9x - 1 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
Step 1: Set the function equal to zero.
[tex]\[ 27x^3 - 27x^2 + 9x - 1 = 0 \][/tex]
Step 2: Solve this cubic equation for [tex]\( x \)[/tex]. The cubic equation can be challenging to solve by hand, but after solving, we find that [tex]\( x = \frac{1}{3} \)[/tex] is a root of the equation.
Therefore, the zero of the function [tex]\( f(x) = 27x^3 - 27x^2 + 9x - 1 \)[/tex] is:
[tex]\[ x = \frac{1}{3} \][/tex]
This is the value of [tex]\( x \)[/tex] that makes the function equal to zero.
To find the zeros of the function [tex]\( f(x) = 27x^3 - 27x^2 + 9x - 1 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex].
Step 1: Set the function equal to zero.
[tex]\[ 27x^3 - 27x^2 + 9x - 1 = 0 \][/tex]
Step 2: Solve this cubic equation for [tex]\( x \)[/tex]. The cubic equation can be challenging to solve by hand, but after solving, we find that [tex]\( x = \frac{1}{3} \)[/tex] is a root of the equation.
Therefore, the zero of the function [tex]\( f(x) = 27x^3 - 27x^2 + 9x - 1 \)[/tex] is:
[tex]\[ x = \frac{1}{3} \][/tex]
This is the value of [tex]\( x \)[/tex] that makes the function equal to zero.
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