Update app.py

app.py

@@ -119,7 +119,7 @@ def solve_polynomial(image, llm_url):
             root_strs.append(str(root_val))
         output += "\\end{aligned}\n$$\n"
 
-        # 🔍 Build structured LLM prompt
+        # 👇 Build structured prompt
         prompt = ""
         try:
             coeffs = sp.Poly(lhs, x).all_coeffs()
@@ -137,10 +137,10 @@ def solve_polynomial(image, llm_url):
                             f"Equation: {lhs} = 0\n"
                             f"Factor: {factor} = 0\n"
                             f"Roots: {root_strs}\n\n"
-                            f"Middle-term factorization used: "
+                            f"This was solved using middle-term factorization:\n"
                             f"a = {a}, b = {b}, c = {c}, a*c = {prod}. "
                             f"{m} and {n} satisfy m*n = ac and m+n = b.\n"
-                            f"Explain clearly, step-by-step.\n<|end|>"
+                            f"Explain the process step-by-step in friendly, simple language."
                         )
                         break
                 if not found:
@@ -152,9 +152,8 @@ def solve_polynomial(image, llm_url):
                 f"Equation: {lhs} = 0\n"
                 f"Factor: {factor} = 0\n"
                 f"Roots: {root_strs}\n\n"
-                f"Middle-term factorization was not suitable.\n"
-                f"Used Sreedhar Acharya quadratic formula instead.\n"
-                f"Explain this step-by-step.\n<|end|>"
+                f"This was solved using the quadratic formula (Sreedhar Acharya method). "
+                f"Explain the process step-by-step in friendly, simple language."
             )
 
         return output, cleaned_latex, prompt
@@ -197,7 +196,8 @@ def solve_from_coeffs(degree, coeff_str):
             f"Equation: {equation_str}\n"
             f"Factor: {factored_str} = 0\n"
             f"Roots: {roots_str}\n\n"
-            f"Explain the above solution in simple steps.\n<|end|>"
+            "Explain the solution step-by-step in human language. "
+            "These roots are correct (up to approximation), so base your reasoning on them."
         )
 
         return result, llm_prompt