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Choose $1$ if the question can be answered by one of the statements alone but not by the other.

Choose $2$ if the question can be answered by using either statement alone.

Choose $3$ if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Choose $4$ if the question cannot be answered even by using both the statements together.

What are the unique values of $b$ and $c$ in the equation $4x^2 + bx + c =0$ if one of the roots of the equation is $- \left(\frac{1}{2} \right)?$

1. The second root is $\frac{1}{2}$
2. the ratio of $c$ and $b$ is $1.$

1