Question

Let α and β be two roots of the equation x² + 2x + 2 = 0, then α¹⁵ + β¹⁵ is equal to : (A) –256 (B) 512
(C) –512 (D) 256
[JEE Main 2019]

Answer 1

Answer:

Correct answer is option (A) -256

Step-by-step explanation:

Given-

x² + 2x + 2 = 0

Now, using the quadratic formula

x^1,2 = ( -b ± √ b² - 4ac ) / 2a

x = ( -2 + √ (2²-4 • 1•2) )/ 2•1 : -1 + i

x = ( -2 - √ ( 2² - 4•1•2)) / 2• 1 : -1 - i

so, roots α = (-1 + i ) and β = (- 1 -i )

Now we need to find

α^15 + β^15

=> ( -1 + i )^15 + ( -1 - i )^15

=> ( - 128 - 128i) + ( -128 + 128i)

=> - 256