Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start $x^2+4x+\cdots$. The ratio of the discriminant, $b^2-4ac$, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start $x^2+4x+\cdots$. The ratio of the discriminant, $b^2-4ac$, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
Eric and Charles each think of a quadratic polynomial. To their surprise, both quadratics start $x^2+4x+\cdots$. The ratio of the discriminant, $b^2-4ac$, of Eric's polynomial to the discriminant of Charles's polynomial is equal to the ratio of Charles's constant term to Eric's constant term. If their constant terms are not equal, find the sum of the constant terms.
train