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Compare Quantity I and Quantity II. Quantity I: $x^2 + x - 6 = 0$ Quantity II: $y^2 + 7y + 12 = 0$

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I ≥ Quantity II
4. Quantity I ≤ Quantity II

Correct answer: Quantity I ≥ Quantity II

Solution

The first equation factors as $(x+3)(x-2)=0$, so its roots are $x=2,-3$. The second factors as $(y+3)(y+4)=0$, so its roots are $y=-3,-4$. Comparing the possible values shows Quantity I is not less than Quantity II.

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