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Algebra
Quadratic Equations
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RRB NTPC Graduate Tier 1 2025 Shift-1 📅 09 Jun, 2025

Find roots of 5m2 + 18m + 16 = 0

A
8/5 and 4
B
-8/5 and -4
C
-8/5 and -2
D
8/5 and 2
Result Summary
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RRB NTPC Graduate Tier 1
2025 • 09 Jun, 2025 • Shift-1
Find roots of 5m2 + 18m + 16 = 0
Correct Answer
-8/5 and -2
Quadratic Factoring Strategy: We need to factor the quadratic equation 5m2 + 18m + 16 = 0. We must find two numbers that multiply to yield (5 * 16) = 80, and ad......
Ref/Book : RRB NTPC Graduate Tier 1 2025
Ref. Subject Algebra
Chapter -
Ref. Topic Quadratic Equations
Pg. No -
💡 Analysis & Explanation
Quadratic Factoring Strategy ▼
We need to factor the quadratic equation 5m2 + 18m + 16 = 0. We must find two numbers that multiply to yield (5 * 16) = 80, and add up to yield the middle coefficient, 18.
Identifying Factors ▼
The two numbers that satisfy both mathematical conditions are 10 and 8 (since 10 * 8 = 80, and 10 + 8 = 18).
Splitting the Middle Term ▼
Rewrite the equation as 5m2 + 10m + 8m + 16 = 0. Grouping the terms gives: 5m(m + 2) + 8(m + 2) = 0. This factors perfectly into (5m + 8)(m + 2) = 0.
Solving for Roots ▼
Setting each binomial factor to zero gives m + 2 = 0 (so m = -2) and 5m + 8 = 0 (so m = -8/5).
Conclusion ▼
The exact mathematical roots are -8/5 and -2.
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