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Equation I: $x^{2} - 9 x + 20 = 0$ . Equation II: $y^{2} - 13 y + 42 = 0$ . Which relation between $x$ and $y$ is always true?

Competition practiceQuadratic Comparison

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

Step-by-Step Solution

I:

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

, so

x = 4

or 5. II:

(y - 6) (y - 7) = 0

, so

y = 6

or 7. Every

x

is smaller than every

y

, so

x < y

.

Answer: C)

x < y

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Solve both equations and compare x and y. I: x² − 17x + 72 = 0. II: y² − 6y + 8 = 0.I: x² − 23x + 132 = 0. II: y² − 21y + 110 = 0. Find how x and y are related.Solve both equations and compare x and y. I: x² − 12x + 32 = 0. II: y² − 6y + 8 = 0.Find the relation between x and y from I: x² − 17x + 72 = 0 and II: y² − 19y + 90 = 0.Work out both quadratics and relate x to y. I. x² − 12x + 35 = 0 II. y² − 9y + 20 = 0