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The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.
Given function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].
Function is a relationship between two or more variables expressed in equal to form.
The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.
The polynomial function is given as:
[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]
factorize the above function
[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]
Now put the function f(x) equal to zero.
f(x)=(2x+9)(5x-3)(x-1)
split the function means put all the expressions equal to zero as under:
(2x+9)(5x-3)(x-1)=0
solve each for the value of x
x=-9/2,x=3/5,x=1
Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.
Learn more about function at https://brainly.com/question/10439235
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