Quadratic Equations

Quantitative Aptitude (SBI-PO)

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Direction: In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

I. x2 − 14x + 13 = 0

II. y2 − 12y + 11 = 0

y > x

x > y

x ≤ y

x ≥ y

x = y or no relation can be established

Explanation:

I. x² − 14x + 13 = 0

⇒ x² − 13x − x + 13 = 0

⇒ x(x − 13) − 1(x − 13) = 0

⇒ (x − 13)(x − 1) = 0

⇒ x = 1, 13

II. y² − 12y + 11 = 0

⇒ y² − 11y − y + 11 = 0

⇒ y(y − 11) − 1(y − 11) = 0

⇒ (y − 11)(y − 1) = 0

⇒ y = 1, 11

Thus, no relation can be established.

By: Munesh Kumari

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