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Given I. $x^{2} + x - 20 = 0$
II. $y^{2} - 11 y + 30 = 0$ , how are $x$ and $y$ related?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

(x + 5) (x - 4) = 0

, so

x = 4

or −5. II:

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

, so

y = 5

or 6. The largest

x

(4) is still below the smallest

y

(5), so

x < y

.

Answer: B)

x < y

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