Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsEasy2 minQB

MathematicsEasysingle choice

If $α$ and $β$ are the roots of the equation $x^{2} - x + 1 = 0$ then $α^{2009} + β^{2009} =$

Answer:

Solution:

The roots of $x^{2} - x + 1 = 0$ are $- ω$ and $- ω^{2}$ .

So, $α^{2009} + β^{2009} = (- ω)^{2009} + (- ω^{2})^{2009} = - ω^{2009} - ω^{4018}$ .

$α^{2009} + β^{2009} = - ω^{2} - ω = - (- 1) = 1$ .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: QB

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