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Compare the roots of I. $x^{2} - 8 x + 15 = 0$
II. $y^{2} - 4 y + 3 = 0$ . What can be said about $x$ and $y$ ?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

(x - 3) (x - 5) = 0

, so

x = 3

or 5. II:

(y - 1) (y - 3) = 0

, so

y = 1

or 3. The smallest

x

(3) equals the largest

y

(3), so

x

≥

y

.

Answer: A)

x

≥

y

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