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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

What is the discriminant of the equation x² - 2x + 13 = 0? Also, determine how many real solutions this equation has.

A
44, Two real roots
B
-48, No real roots
C
40, Two equal roots
D
46, One real root
Result Summary
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APEDIA

NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
What is the discriminant of the equation x² - 2x + 13 = 0? Also, determine how many real solutions this equation has.
Correct Answer
-48, No real roots
Coefficient Extraction: A standard quadratic equation formats as ax² + bx + c = 0. Extracting variables gives a = 1, b = -2, and c = 13.Discriminant Formula: T......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Coefficient Extraction ▼
A standard quadratic equation formats as ax² + bx + c = 0. Extracting variables gives a = 1, b = -2, and c = 13.
Discriminant Formula ▼
The exact nature of quadratic roots is calculated exclusively using the discriminant threshold formula: D = b² - 4ac.
Numerical Execution ▼
Plugging in the extracted values gives D = (-2)² - 4(1)(13) = 4 - 52 = -48.
Root Property Analysis ▼
When the calculated discriminant (D) is a strictly negative integer (D < 0), the equation geometrically fails to intersect the x-axis, meaning it possesses zero real roots.
Conclusion ▼
The discriminant is -48, dictating absolutely no real solutions.
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