Question
Question: If α, β are the roots of $x^2 - 2x + 4 = 0$ then α⁵ + β⁵ =...
If α, β are the roots of x2−2x+4=0 then α⁵ + β⁵ =
A
4
B
8
C
16
D
32
Answer
32
Explanation
Solution
The roots of the quadratic equation are found and converted to polar form. De Moivre's theorem is applied to calculate the fifth powers of the roots, and then these powers are summed. Alternatively, a recurrence relation derived from the quadratic equation is used to find the sum of powers.