Solve (x-4.4)(x-2.3) > 0: Finding Positive Values of a Quadratic Function

To solve this problem, we need to analyze where the expression $(x - 4.4)(x - 2.3)$ is greater than zero. We have two roots, $x = 4.4$ and $x = 2.3$, which divide the number line into three intervals: $x < 2.3$, $2.3 < x < 4.4$, and $x > 4.4$.

Let's check these intervals:

• For $x < 2.3$, both $(x - 4.4)$ and $(x - 2.3)$ are negative, resulting in a positive product.
• For $2.3 < x < 4.4$, $(x - 4.4)$ is negative and $(x - 2.3)$ is positive, resulting in a negative product.
• For $x > 4.4$, both $(x - 4.4)$ and $(x - 2.3)$ are positive, resulting in a positive product.

Thus, the expression $(x - 4.4)(x - 2.3) > 0$ holds in the intervals $x < 2.3$ and $x > 4.4$.

Therefore, the solution is $x > 4.4$ or $x < 2.3$.