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Equation I: $x^{2} - 16 x + 60 = 0$ . Equation II: $y^{2} - 9 y + 18 = 0$ . Which relation between $x$ and $y$ is true?

Competition practiceQuadratic Comparison

A $x > y$
B $x$ ≥ $y$
C $x$ ≤ $y$
Drelation cannot be established

Step-by-Step Solution

I:

(x - 6) (x - 10) = 0

, so

x = 6

or 10. II:

(y - 3) (y - 6) = 0

, so

y = 3

or 6. The smallest

x

(6) equals the largest

y

(6), so

x

≥

y

.

Answer: B)

x

≥

y

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