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Quantitative Aptitude
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NTPC Graduate Tier 1 2025 Shift-3 📅 05 Jun, 2025

If sum and product of the roots of a quadratic equation are (4 - 3√2) and -28, respectively, then find the quadratic equation.

A
x² - (4 + 3√2)x + 28 = 0
B
x² + (4 + 3√2)x + 28 = 0
C
x² + (4 - 3√2)x - 28 = 0
D
x² - (4 - 3√2)x - 28 = 0
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-3
If sum and product of the roots of a quadratic equation are (4 - 3√2) and -28, respectively, then find the quadratic equation.
Correct Answer
x² - (4 - 3√2)x - 28 = 0
[Algebraic Foundation Setup]: A fundamental theorem of polynomials states that any standard quadratic equation can be universally constructed using its roots vi......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Quantitative Aptitude
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
[Algebraic Foundation Setup] ▼
A fundamental theorem of polynomials states that any standard quadratic equation can be universally constructed using its roots via the template: x² - (Sum of Roots)x + (Product of Roots) = 0.
[Component Identification] ▼
The problem explicitly defines the 'Sum of Roots' variable as the complex expression (4 - 3√2). Furthermore, it provides the 'Product of Roots' variable as the negative integer -28.
[Template Assembly] ▼
Carefully substituting these exact given values into their respective slots within the standard template generates the raw equation.
[Final Equation Structure] ▼
The linear 'x' term takes the negative of the sum, becoming -(4 - 3√2)x. The constant term takes the exact product, becoming -28.
Conclusion ▼
The perfectly assembled equation is x² - (4 - 3√2)x - 28 = 0.
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