Question

If h(x) = 3(x - 1)², find all values of x for which h(x) = -108.

a) x = 8
b) x = -8
c) x = 9
d) x = -9

Answer 1

There are no real solutions for x that satisfy the equation h(x) = -108, as the square of a real number cannot be negative.

Step-by-step explanation:

If h(x) = 3(x - 1)², we are to find all values of x for which h(x) = -108. First, we set the equation equal to -108 and solve for x:

3(x - 1)² = -108

Divide both sides by 3 to isolate the squared term:

(x - 1)² = -36

We can now see there is a discrepancy because the square of a real number cannot be negative. Therefore, there are no real solutions for x that will satisfy the equation h(x) = -108 as the result of squaring a real number is always non-negative.