Let and be two roots of the equation x^2 + 2x + 2 = 0, then is equal to

JEE MainMathematicsToughQuadratic Equations

Let $\alpha$ and $\beta$ be two roots of the equation x^2 + 2x +
2 = 0, then $\alpha^{15}\ + \beta^{15}$ is equal to

Show answer and solution

Roots are -1 + i and -1 - i
Let

\alpha

= -1 + i and β = -1 - i
Then,

\alpha^{15} + \beta^{15} = ( - 1 + i)^{15} + ( - 1 - i)^{15} = \frac{( - 1 + i)^{16}}{3 - 1 + i} + \frac{( - 1 - i)^{16}}{- 1 - i} = 2^{8}\frac{( - 1 + i - 1 - i)^{16}}{1^{2} - i^{2}}

= 128( - 2) = - 256

Source: Grass-G / M-22 Mathematics Paper 19 Dec Eng.docx

Scan any doubt from your notes and get a whiteboard explanation.