1. **State the problem:** Given the quadratic function $f(x) = (a-2)x^2 + (b+3)x + (c-2)$, we are told it is zero degree and its range is 5. We need to find $a+b+c$. 2. **Understand zero degree:** A zero degree polynomial means the function is a constant, so the coefficients of $x^2$ and $x$ must be zero. 3. **Set coefficients to zero:** - Coefficient of $x^2$: $a-2=0 \implies a=2$ - Coefficient of $x$: $b+3=0 \implies b=-3$ 4. **Function becomes constant:** $$f(x) = c-2$$ 5. **Range is 5:** Since $f(x)$ is constant, its range is just the constant value. So, $$c-2 = 5 \implies c = 7$$ 6. **Find $a+b+c$:** $$a+b+c = 2 + (-3) + 7 = 6$$ **Final answer:** $a+b+c=6$