Q61.Let α1, α2, … , α7α1, α2, … , α7 be the roots of the equation x7 + 3x5 −13x3 −15x = 0 and |α1| ≥|α2| ≥… ≥|α7|. Then, α1α2 −α3α4 + α5α6 is equal to _______ ¯
What This Question Tests
This question tests the ability to find roots of a higher-degree polynomial by factoring and substitution, followed by ordering them based on magnitude and calculating a specific expression involving these roots. It requires careful handling of complex roots.
Concepts Tested
Formulas Used
For P(x) = a_n x^n + ... + a_0 = 0, product of roots = (-1)^n a_0 / a_n
Factoring cubic polynomials
📚 NCERT Sections This Tests
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of polynomial equations
- Year
- 2023
- Shift
- 29 Jan Shift 2
- Q Number
- Q61
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers; Class 11 Mathematics Ch 2: Polynomials (implied)
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