Question

What is the solution set of the quadratic inequality 4(x + 2)2 <0?

a.. x
b. x = R
c. x=2

Answer 1

The solution set for the inequality 4(x + 2)²< 0 is empty because a square of a real number multiplied by a positive number cannot be less than zero.

Step-by-step explanation:

The quadratic inequality in question is 4(x + 2)² < 0. To find the solution set, we first observe that a square of any real number is always non-negative (greater than or equal to zero).

This means that 4(x + 2)² is non-negative because it is a square multiplied by a positive number (4).

However, the inequality is asking for the expression to be strictly less than zero, which is impossible for a square of a real number. Therefore, there are no real values of x that satisfy this inequality, and the solution set is empty.