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Complex Numbers and Quadratic Equations

JEE Main 2024 (Online) 27th January Evening ShiftMCQEasy📈 Topic in 34% papers+4−1
Ques. 1JEE Main 2024, 27 January (Evening Shift)

If , are the roots of the equation, x2-x-1=0 and Sn=2023 n+2024 n, then :

  1. 2S12=S11+S10
  2. S12=S11+S10
  3. S11=S10+S12
  4. 2S11=S12+S10

Answer

(2) S12=S11+S10

Solution

2= +1 n= n-1+ n-2 (multiply by n-2); same for

2023 n+2024 n= (2023 n-1+2024 n-1 )+ (2023 n-2+2024 n-2 )

Sn=Sn-1+Sn-2

Put n=12: S12=S11+S10

Answer: (2)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2024, 27 January (Evening Shift)

Let the complex numbers and 1 lie on the circles |z-z0 |2=4 and |z-z0 |2=16 respectively, where z0=1+i. Then, the value of 100| |2 is .

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