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SSC & BANK EXAMS: QUANTITATIVE APTITUDE · QUADRATIC EQUATIONS

Quadratic equations: compare x and y (bank exams)

Solve both equations by factorising, then compare every root of x with every root of y.

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Worked examples

Example 1 · level 1

I. x² − 7x + 10 = 0 II. y² − 15y + 56 = 0 Find the relation between x and y.

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or relationship cannot be established
Show solution
  1. I: x = 5, 2.
  2. II: y = 7, 8.
  3. Comparing: every value of x is less than every value of y.
  4. Answer: x < y.

Answer: x < y

Example 2 · level 2

I. x² − 9x + 8 = 0 II. y² + 7y + 6 = 0 Find the relation between x and y.

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or relationship cannot be established
Show solution
  1. I: x = 8, 1.
  2. II: y = −1, −6.
  3. Comparing: every value of x is greater than every value of y.
  4. Answer: x > y.

Answer: x > y

Example 3 · level 3

I. 2x² + 5x + 2 = 0 II. 2y² − 5y − 3 = 0 Find the relation between x and y.

  1. x > y
  2. x < y
  3. x ≥ y
  4. x ≤ y
  5. x = y or relationship cannot be established
Show solution
  1. I: x = −1/2, −2.
  2. II: y = 3, −1/2.
  3. Comparing: no x is bigger than any y, and the largest x equals the smallest y.
  4. Answer: x ≤ y.

Answer: x ≤ y

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