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NTPC Graduate Tier 1 2025 Shift-1 📅 06 May, 2025

Find the value of K if the quadratic equations 2x² + Kx + 8 = 0 and 3x² + 4x + 12 = 0 have both roots common.

A
8/3
B
4/3
C
5/3
D
7/3
Result Summary
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NTPC Graduate Tier 1
2025 • 06 May, 2025 • Shift-1
Find the value of K if the quadratic equations 2x² + Kx + 8 = 0 and 3x² + 4x + 12 = 0 have both roots common.
Correct Answer
8/3
Condition for Identical Roots: When two quadratic equations (a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0) share both roots, their coefficients are......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Condition for Identical Roots ▼
When two quadratic equations (a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0) share both roots, their coefficients are strictly proportional.
Ratio Setup ▼
This implies the relation a₁/a₂ = b₁/b₂ = c₁/c₂ must hold true.
Applying Values ▼
Substituting the given coefficients, we get 2/3 = K/4 = 8/12. Simplifying 8/12 confirms the ratio is 2/3.
Solving for Variable ▼
Equating the middle term, K/4 = 2/3, which leads to K = (2*4)/3 = 8/3.
Conclusion ▼
The exact value required for K is 8/3.
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