The actual roots of the function are -9/2, 3/5 and 1
The roots of a polynomial function are the zeros of the polynomial function.
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]
Set the function to 0
[tex](2x + 9)(5x - 3)(x - 1) = 0[/tex]
Split the function, as follows:
[tex]2x + 9 = 0,\ 5x - 3 = 0,\ x - 1 = 0[/tex]
Solve for x in each case
[tex]x= -9/2,\ x = 3/5,\ x = 1[/tex]
Hence, the actual roots of the function are -9/2, 3/5 and 1
Read more about rational root theorem at:
https://brainly.com/question/10937559
