Q81.Let ๐ผ, ๐ฝ๐ผ> ๐ฝ be the roots of the quadratic equation ๐ฅ2 - ๐ฅ- 4 = 0. If ๐๐= ๐ผ๐- ๐ฝ๐, ๐โโ, then ๐15๐16 - ๐14๐16 - ๐152 + ๐14๐15 is equal to _____. ๐13๐14
What This Question Tests
This question tests the application of the property that roots of a quadratic equation satisfy the equation, leading to a recurrence relation for terms like P_n = ฮฑโฟ - ฮฒโฟ, which simplifies the complex expression.
Concepts Tested
Formulas Used
ฮฑยฒ - ฮฑ - 4 = 0
ฮฒยฒ - ฮฒ - 4 = 0
ฮฑ+ฮฒ=1, ฮฑฮฒ=-4
๐ NCERT Sections This Tests
13.5 โ The Q Value Of A Nuclear Reaction A + B ยฎ C + D Is Defined By
Physics Class 12 ยท Chapter 13
13.5 The Q value of a nuclear reaction A + b ยฎ C + d is defined by Q = [ mA + mb โ mC โ md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H โ12 H+12 H (ii) 126 C+126 C โ1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
9.15 โ Apply Mirror Equation And The Condition:
Physics Class 12 ยท 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.
14.2 โ Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 ยท Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
๐ Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of quadratic equations and recurrence relations
- Year
- 2022
- Shift
- 29 Jul Shift 2
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 10 Mathematics Ch 4: Quadratic Equations; Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations (advanced topics)
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