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Determine the relation between $x$ and $y$ : I. $2 x^{2} - 25 x + 78 = 0$
II. $y^{2} - 11 y + 30 = 0$

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

(2 x - 13) (x - 6) = 0

, so

x = 6.5

or 6. II:

(y - 5) (y - 6) = 0

, so

y = 5

or 6. The smallest

x

(6) equals the largest

y

(6), so

x

≥

y

.

Answer: B)

x

≥

y

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