Provide an Appropriate Response $k , a , b$ , And $c$

Multiple Choice

Provide an appropriate response.
-Suppose that $k , a , b$ , and $c$ are real numbers and that the polynomial function $f$ may be expressed in factored form as $f ( x ) = ( x - k ) \left( a x ^ { 2 } + b x + c \right)$ . If $b ^ { 2 } - 4 a c = - 57$ , determine the number of real and imaginary zeros that $f$ has.

A) 3 real zeros, 0 imaginary zeros
B) 2 real zeros, 2 imaginary zeros
C) 2 real zeros, 1 imaginary zero
D) 1 real zero, 2 imaginary zeros