Provide an Appropriate Response $a$ $b$ , And $c$ Are Real Numbers and That the Polynomial Function

Multiple Choice

Provide an appropriate response.
-Suppose that $a$ , $b$ , and $c$ are real numbers and that the polynomial function $\mathrm { f }$ may be expressed in factored form as $f ( x ) = ( 13 x - 7 ) ( 14 x + 5 ) \left( a x ^ { 2 } + b x + c \right)$ . If $b ^ { 2 } - 4 a c = 169$ , determine the number of rational, irrational, and imaginary zeros that $f$ has.

A) 2 rational zeros, 2 irrational zeros, 0 imaginary zeros
B) 4 rational zeros, 0 irrational zeros, 0 imaginary zeros
C) 2 rational zeros, 0 irrational zeros, 2 imaginary zeros
D) 0 rational zeros, 0 irrational zeros, 4 imaginary zeros