• Numerical Ability - Quadratic Equations
Question

I. 8x² + 6x = 5

II. 12y² – 22y + 8 = 0

  • A) if x < y
  • B) if x ≤ y
  • C) relationship between x and y cannot be determined
  • D) if x ≥ y
  • E) if x > y
Solution

Sol.

I. 8x² + 6x – 5 = 0 ⇒ 8x² + 10x – 4x – 5 = 0 ⇒ (4x + 5) (2x – 1) = 0 ⇒ x = ½, –5/4

II. 12y² – 22y + 8 = 0 ⇒ 6y² – 11y + 4 = 0 ⇒ 6y² – 3y – 8y + 4 = 0 ⇒ (2y – 1) (3y – 4) = 0 ⇒ y = 1/2, 4/3 y ≥ x

Sol.

I. 8x² + 6x – 5 = 0 ⇒ 8x² + 10x – 4x – 5 = 0 ⇒ (4x + 5) (2x – 1) = 0 ⇒ x = ½, –5/4

II. 12y² – 22y + 8 = 0 ⇒ 6y² – 11y + 4 = 0 ⇒ 6y² – 3y – 8y + 4 = 0 ⇒ (2y – 1) (3y – 4) = 0 ⇒ y = 1/2, 4/3 y ≥ x
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