Question

Solve x² (x + 2)(x - 5) = 0

Answer 1

The equation x² (x + 2)(x - 5) = 0 is solved by setting each factor equal to zero and solving for x, yielding the solutions x = 0, x = -2, and x = 5.

Step-by-step explanation:

To solve the equation x² (x + 2)(x - 5) = 0, we need to find the values of x for which the product of these three factors equals zero. According to the zero product property, if the product of multiple factors equals zero, then at least one of the factors must be zero.

Step 1: Set each factor equal to zero:

• x² = 0
• x + 2 = 0
• x - 5 = 0

Step 2: Solve each equation separately:

1. x² = 0 → x = 0
2. x + 2 = 0 → x = -2
3. x - 5 = 0 → x = 5

Therefore, the solution to the equation x² (x + 2)(x - 5) = 0 is x = 0, x = -2, and x = 5.