Question

Find all values of c such that the domain of the following function is the set of all real numbers

Answer 1

Answer:

$-\sqrt{14} < c < \sqrt{14}$

Step-by-step explanation:

For the function to have a domain of all reals, the denominator cannot have a value of zero. x^2 + 2cx + 14 will not have zero as a root if it has no real solutions. A quadratic equation has no solutions when the discriminant is negative.

b^2 - 4ac < 0

(2c)^2 - 4(1)(14) < 0

4c^2 - 56 < 0

4c^2 < 56

c^2 < 14

$-\sqrt{14} < c < \sqrt{14}$