1. **State the problem:** We are given a function $f(x) = 4x^2 - 5x + 7$ and asked to find where $h \neq o$. 2. **Clarify the problem:** The notation $h \neq o$ is unclear in the context of the function $f$. Assuming the question is to find where $f(x) \neq 0$, i.e., find the values of $x$ for which the function is not zero. 3. **Set the function equal to zero to find roots:** $$4x^2 - 5x + 7 = 0$$ 4. **Use the quadratic formula:** For $ax^2 + bx + c = 0$, the roots are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=4$, $b=-5$, and $c=7$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 4 \times 7 = 25 - 112 = -87$$ 6. **Interpret the discriminant:** Since $\Delta < 0$, there are no real roots. This means $f(x) \neq 0$ for all real $x$. 7. **Conclusion:** The function $f(x)$ never equals zero for any real number $x$, so $f(x) \neq 0$ everywhere on the real line. **Final answer:** $f(x) \neq 0$ for all real $x$.