Finding Polynomial Coefficients from Conditions

Consider the polynomial function:

$$P(x) = 2x^4 - 3x^3 + ax^2 + bx + c$$

It is given that:

• The polynomial has a root at $x = 1$.
• The value of the polynomial at $x = 2$ is 5.

If $a$, $b$, and $c$ are constants, which of the following sets of values for $(a, b, c)$ satisfies the conditions given?