algebra precalculus - Solve the equation $x^4-2x^3-21x^2+22x+40=0$ whose roots are in A.P. - Mathematics Stack Exchange

Solve the equation $x^4-2x^3-21x^2+22x+40=0$ whose roots are in A.P. (arithmetic progression). I don't understand this solution. Why are the terms of AP considered as mentioned in the question and

solve the equation x^4-2x^3-21x^2+22x+40=0 whose roots are in arithmetical progression ​

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Solved Solve x4-2x3-21x2+22x+40=0, whose roots are in

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find the roots of equation x^4+2x^3-21x^2-22x+40=0 if they are in a.p.​

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32. Two roots of the equation ( x ^ { 4 } - 6 x ^ { 3 } + 18 x ^ { 2 } - 30 x + 25 = 0 ) are of the form ( alpha + i beta ) and ( beta + i alpha . ) Find all the roots of the equation.

4 x ^ { 3 } - 24 x ^ { 2 } + 23 x + 18 = 0 , ) the rous being in ( A ) ( x ^ { 3 } - 7 x ^ { 2 } + 14 x - 8 = 0 , ) the roots boing in ( G )

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