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NTPC Graduate Tier 1 2025 Shift-2 📅 06 Jun, 2025

Factorise the polynomial x⁴ - 10x² + 22 into product of two quadratic polynomials.

A
(x² - 4 + √3)(x² - 4 - √3)
B
(x² - 3 + √3)(x² - 3 - √3)
C
(x² - 2 + √3)(x² - 2 - √3)
D
(x² - 5 + √3)(x² - 5 - √3)
Result Summary
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NTPC Graduate Tier 1
2025 • 06 Jun, 2025 • Shift-2
Factorise the polynomial x⁴ - 10x² + 22 into product of two quadratic polynomials.
Correct Answer
(x² - 5 + √3)(x² - 5 - √3)
Completing the Square Strategy: The given mathematical expression is a biquadratic polynomial: x⁴ - 10x² + 22. We can strategically manipulate this form by a......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Completing the Square Strategy ▼
The given mathematical expression is a biquadratic polynomial: x⁴ - 10x² + 22. We can strategically manipulate this form by adding and subtracting 3 to forcibly complete a perfect square structure: x⁴ - 10x² + 25 - 3.
Forming Algebraic Identities ▼
The first three distinct terms now perfectly group to form a completed square: (x² - 5)². The total expression is now written as (x² - 5)² - 3, which can be further represented as (x² - 5)² - (√3)².
Applying Difference of Squares ▼
Using the fundamental algebraic identity a² - b² = (a - b)(a + b), where our specific parameters are a = (x² - 5) and b = √3, we can successfully factorize the entire expression.
Final Expansion ▼
Neatly substituting the parameter values back gives the final, cleanly factorized form: (x² - 5 + √3)(x² - 5 - √3).
Conclusion ▼
The accurately factorized form matches option four.
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