Sum of roots =4a+3a=7a=−b Or b=−7a Product of roots =4a×3a=c Or c=12a2 Now, b2+c=(−7a)2+12a2=61a2 Comparing the options. Option 1: 61a2=3721⇒a2=61, clearly a is not an integer. Option 2: 61a2=549⇒a2=9, we can have a=−3 or 3 (an integer) Option 3: 61a2=427⇒a2=7, clearly a is not an integer. Option 4: 61a2=361⇒a2=‌