Q61.Let α, β be the roots of the equation x2 + 2√2x −1 = 0. The quadratic equation, whose roots are α4 + β4 and 1 (α6 + β6), is : 10 (1) x2 −190x + 9466 = 0 (2) x2 −180x + 9506 = 0 (3) x2 −195x + 9506 = 0 (4) x2 −195x + 9466 = 0
What This Question Tests
Tests the ability to find powers of roots of a quadratic equation using sum and product of roots, and then construct a new quadratic equation from these derived roots.
Concepts Tested
Formulas Used
α+β = -b/a
αβ = c/a
α^2+β^2 = (α+β)^2 - 2αβ
α^3+β^3 = (α+β)(α^2+β^2-αβ)
α^4+β^4 = (α^2+β^2)^2 - 2(αβ)^2
α^6+β^6 = (α^3+β^3)^2 - 2(αβ)^3
📚 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.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
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.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of quadratic equations
- Year
- 2024
- Shift
- 09 Apr Shift 1
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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