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#Maths
#Complex numbers and quadratic equations
#Engineering
#Joint Entrance Examination Main

If α, β $\epsilon$ C are the distinct roots, of the equation x²−x+1=0, then α¹⁰¹+β¹⁰⁷ is
equal to:

Option 1)
$2$

Option 2)
$-1$

Option 3)
$0$

Option 4)
$1$

Answers (1)

@5337

Roots of $x^{2}-x+1=0$

are

$-\omega$ are $-\omega ^{2}$

thus $-\omega ^{101}+ (-\omega ^{2})^{107}$

$-\omega ^{2}+ (-\omega ^{2})^{2}$

$-\omega ^{2} -\omega=1$

Option 1)

$2$

Option 2)

$-1$

Option 3)

$0$

Option 4)

$1$

Posted by

perimeter

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If α, β C are the distinct roots, of the equation x2−x+1=0, then α101+β107 is equal to: Option 1) Option 2) Option 3) Option 4)

Answers (1)

Posted by

perimeter

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If α, β $\epsilon$ C are the distinct roots, of the equation x²−x+1=0, then α¹⁰¹+β¹⁰⁷ is
equal to:

Option 1)
$2$

Option 2)
$-1$

Option 3)
$0$

Option 4)
$1$