Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.)

Question

Square root of (x^2 -4x-60). Need answer in interval notation. thanks!

Answer 1

For the square root of (x² -4x-60) be a real number, (x² -4x-60) must be greater than zero, so we have:

x² -4x-60 > 0

x² -4x + 4- 64 > 0

(x-2)² > 64

Then we have:

x-2 > 8 or x-2 < -8

x > 10 or x < -6

Therefore we have:

{x ∈ ℜ/ x > 10 or x < -6 }