Find the Interval(s)for B Such That the Equation Has at Least

question 42

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 \(b \leq 2 \sqrt { a c }\)

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