Find the Interval(s) for B Such That the Equation Has $4 x ^ { 2 } + b x + 7 = 0$

Multiple Choice

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients
$4 x ^ { 2 } + b x + 7 = 0$ .

A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c < 0$ , $b \geq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
B) $( - \infty , - 2 \sqrt { 28 } ] \cup [ - 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$
C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$