ExamHabit
Practise free

JEE Main 2015

JEE Main 2015 Mathematics question on Complex Numbers and Quadratic Equations

Let α\alpha and β\beta be the roots of equation x2−6x−2=0x^2 - 6x - 2 = 0. If an=αn−βna_n = \alpha^n - \beta^n, for n≥1n \geq 1, then the value of a10−2a82a9\dfrac{a_{10} - 2a_8}{2a_9} is
  1. A.
    6
  2. B.
    -6
  3. C.
    3
  4. D.
    -3
Show answer and solution

Correct option: C

Solution

Since α and β are roots of x² - 6x - 2 = 0, we have α² = 6α + 2 and β² = 6β + 2.

Key recurrence: aₙ = αⁿ - βⁿ satisfies aₙ = 6aₙ₋₁ + 2aₙ₋₂ (from the characteristic equation).

So a₁₀ = 6a₉ + 2a₈, which gives a₁₀ - 2a₈ = 6a₉.

Therefore (a₁₀ - 2a₈)/(2a₉) = 6a₉/(2a₉) = 3.

[JEE Main 2015]

Practise Complex Numbers and Quadratic Equations the way it is asked

A timed set of real JEE Main Complex Numbers and Quadratic Equations questions, graded as the exam grades. No sign-up.

Start a Complex Numbers and Quadratic Equations test

More: all JEE Main Complex Numbers and Quadratic Equations questions · JEE Main 2015 · Mathematics chapter list