Question

Tim throws a stick straight up in the air from the ground. What is the greatest possible integer value of x for which sqrt of (x−5) is an imaginary number?

Option 1: 3
Option 2: 4
Option 3: 5
Option 4: 6

Answer 1

The greatest integer value of x for which sqrt(x−5) is imaginary is 4 since it is the largest integer less than 5, making expression negative.

Step-by-step explanation:

The question involves finding the greatest possible integer value of x for which the square root of (x−5) is an imaginary number. By definition, a square root becomes imaginary when its argument is negative. Therefore, for the expression √(x−5) to be imaginary, x−5 must be less than 0. Thus, the greatest possible integer value of x that satisfies this condition is the greatest integer less than 5. The possible integer values are ...4, 3, 2, 1, 0, -1, etc. Hence, the correct answer is Option 2: 4, as it is the greatest integer less than 5.