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Compare the roots of I. $x^{2} - 31 x + 240 = 0$
II. $y^{2} - 29 y + 210 = 0$ . Which relation holds?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I.

(x - 15) (x - 16) = 0

, so

x = 15

or 16. II.

(y - 14) (y - 15) = 0

, so

y = 14

or 15. The smallest

x

(15) equals the largest

y

(15), so

x

≥

y

.

Answer: D)

x

≥

y

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