Root of Polynomial between 1 and 2

Consider the polynomial function defined by the expression:

$$P(x) = 4x^4 - 8x^3 + 5x^2 - 10x + 3$$

Determine the value of $x$ for which the function $P(x)$ is equal to zero and lies between 1 and 2 (exclusive). Provide your answer as a grid-in response to the nearest hundredth.