which inequality represents all values of x for which the quotient below is defined? ✓15(x-1) ÷ ✓2x^2

9514 1404 393

  C.  x ≥ 1

Step-by-step explanation:

The content of the radical must be non-negative in both cases. The square of x is already non-negative for any x.

  15(x -1) ≥ 0

  x -1 ≥ 0 . . . . divide by 15; next, add 1

  x ≥ 1 . . . . . matches choice C

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.