AP EAMCET2008MathematicsQuadratic Equation

The sum of the fourth powers of the roots of the equation x^3+x+1=0 is

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Correct answer

D. 2

Step-by-step solution

Given equation is x^3+x+1=0 On comparing with x^3+p₁ x^2+p₂ x+p₃=0 , we get Now, p₁=0, p₂=1, p₃=1 aligned & S₂+0 S₁+2=0 S₂=-2 & S₃+0 S₂+1 S₁+(2)=0 S₃=-2 & S₄+0 S₃+1 S₂+1 S₁=0 & S₄+0+1(-2)+1(0)=0 & S₄=2 aligned S₁=0, S₀=2

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