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Two quadratics are given: I. $x^{2} - 21 x + 108 = 0$
II. $y^{2} - 27 y + 180 = 0$ . Which relation holds?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

(x - 9) (x - 12) = 0

, so

x = 9

or 12. II:

(y - 12) (y - 15) = 0

, so

y = 12

or 15. The largest

x

(12) equals the smallest

y

(12), so

x

≤

y

.

Answer: A)

x

≤

y

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