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← JEE Main 2022 · 26 Jun · Shift 1
MathematicsInteger+4 / -1Question 21 of 90

JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 21

The sum of the cubes of all the roots of the equation x4−3x3−2x2+3x+1=0x^4-3x^3-2x^2+3x+1=0 is ______.

Answer and worked solution

Official answer: 36

Symmetric sums. e1=3e_1=3, e2=−2e_2=-2, e3=−3e_3=-3.

Newton's identity. ∑α3=e13−3e1e2+3e3=27+18−9=36\sum\alpha^3=e_1^3-3e_1e_2+3e_3=27+18-9=36.

Answer: 36

Topics:Theory of equations (higher degree)
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