Q61.If m is chosen in the quadratic equation (m2 + 1)x2 −3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is: (1) 4√3 (2) 10√5 (3) 8√3 (4) 8√5
What This Question Tests
This question involves finding the value of 'm' that maximizes the sum of roots of a quadratic equation and then using that value to calculate the absolute difference of the cubes of its roots using algebraic identities.
Concepts Tested
Formulas Used
α + β = -b/a
αβ = c/a
(α - β)² = (α + β)² - 4αβ
α³ - β³ = (α - β)((α + β)² - αβ)
📚 NCERT Sections This Tests
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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, Maxima/Minima
- Year
- 2019
- Shift
- 09 Apr Shift 2
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Quadratic Equations
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