Question
Download Solution PDFDirection: In the given question, two equations numbered l and II are given. Solve both equations and mark the appropriate answer.
I. 12x² + 7x − 12 = 0
II. 8y² − 18y + 9 = 0
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFEquation I: 12x² + 7x − 12 = 0
⇒ Discriminant = 7² − 4 × 12 × (−12) = 49 + 576 = 625, √625 = 25
⇒ x = [−7 ± 25] ÷ (2 × 12) = [−7 ± 25] ÷ 24
x₁ = (18) ÷ 24 = 3/4 = 0.75
x₂ = (−32) ÷ 24 = −4/3 ≈ −1.333
Equation II: 8y² − 18y + 9 = 0
⇒ Discriminant = (−18)² − 4 × 8 × 9 = 324 − 288 = 36, √36 = 6
⇒ y = [18 ± 6] ÷ (2 × 8) = [18 ± 6] ÷ 16
y₁ = 24 ÷ 16 = 3/2 = 1.5
y₂ = 12 ÷ 16 = 3/4 = 0.75
Comparison of roots:
x₂ = −1.333 < y₂ = 0.75
x₁ = 0.75 = y₂ = 0.75
x₁ = 0.75 < y₁ = 1.5
x₂ = −1.333 < y₁ = 1.5
All x-values are ≤ all y-values.
Thus, the correct answer is x ≤ y.
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