NTA Abhyas JEE Main2020MathematicsSequences and SeriesPractice
Given α and β are the roots of the quadratic equation x 2 - 4 x + k = 0 k ≠ 0 . If α β ,   α β 2 + α 2 β and α 3 + β 3 are in geometric progression, then the value of k is equal to
Options
- A4
- B16 7
- C3 7
- D12
Correct answer
B. 16 7
Step-by-step solution
Here, α + β = 4 , α β = k α β , α β ( α + β ) and α + β 3 - 3 α β α + β are in G.P. ⇒ 4 k 2 = k 64 - 12 k ⇒ 16 k 2 = 4 k 16 - 3 k ⇒ 4 k = 16 - 3 k ⇒ 7 k = 16 ⇒ k = 16 7