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Solve I. $x^{2} - 15 x + 56 = 0$
II. $y^{2} - 11 y + 28 = 0$ . Which relation between $x$ and $y$ always holds?

Competition practiceQuadratic Comparison

A $x$ ≥ $y$
B $x$ ≤ $y$
C $x < y$
D $x > y$

Step-by-Step Solution

I:

(x - 7) (x - 8) = 0

, so

x = 7

or 8. II:

(y - 4) (y - 7) = 0

, so

y = 4

or 7. The smallest

x

equals the largest

y

(7), so

x

≥

y

.

Answer: A)

x

≥

y

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