Problem

For the rectangle-area model \(A(x)=x(x+6)\) with \(x\ge~0\), find both algebraic zeros. Classify each using the domain, then explain why the admissible zero is a degenerate boundary rather than a positive-area rectangle.

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The algebraic zeros are x = 0 and x = −6. The value −6 is outside x ≥ 0; x = 0 is a degenerate boundary case with area 0, not a positive-area rectangle.

The algebraic zeros are x = 0 and x = −6. Both are valid physical side lengths for zero-area rectangles.

The algebraic zeros are x = 0 and x = 6. Both are valid, and x = 6 gives zero area.

The algebraic zeros are x = 0 and x = −6. A rectangle can have side length −6, so both values are physically meaningful.

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For the rectangle-area model \(A(x)=x(x+6)\) with \(x\ge~0\), find both algebraic zeros. Classify each using the domain, then explain why the admissible zero is a degenerate boundary rather than a positive-area rectangle.

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