Question

Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.) Squareroot (5x2 − 27x + 10)

Answer 1

The expression: sqrt ( 5 x² - 27 x + 10 )
A real number is a square root of a positive number.
x 1/2 = ( 27 +/- sqrt ( 729- 200 )) / 10
x 1/2 = ( 27+/- 23 ) / 10
x 1 = 4/10 = 0.4
x 2 = 50/10 = 5
Answer:
The expression is defined as a real number for:
x ∈ ( - ∞, 0.4 ] ∪ [ 5, + ∞ ).