In each of these questions, two equations are given. Solve both equations and give the answer: (i) $x^2 - 11x + 24 = 0$ (ii) $y^2 - 14y + 45 = 0$

if x > y
if x ≥ y
if x < y
if x ≤ y

Correct answer: if x ≤ y

Solution

The roots of $x^2 - 11x + 24 = 0$ are 3 and 8. The roots of $y^2 - 14y + 45 = 0$ are 5 and 9. Since the smallest possible value of x is 3 and the largest possible value of y is 9, the only definite relation is $x \le y$.

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