In the given question, two equations numbered I and II are given. Solve both equations and mark the appropriate answer. I. $x^2 - 32x + 255 = 0$ II. $y^2 - 23y + 120 = 0$

x > y
x < y
x ≥ y
x ≤ y

Correct answer: x ≥ y

Solution

Equation I factors as $(x-15)(x-17)=0$, so $x=15$ or $17$. Equation II factors as $(y-8)(y-15)=0$, so $y=8$ or $15$. Since the smallest possible $x$ is 15 and the largest possible $y$ is 15, the correct relation is $x \ge y$.

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