Find the root of a cubic function

Consider the function defined by the equation:

$$ f(x) = 3x^3 - 5x^2 + 4x - 2 $$

Determine the value of $$ x $$ for which $$ f(x) = 0 $$ in the interval $$ [1, 2] $$, and enter your answer in the grid below. Round your answer to the nearest hundredth.