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

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The product of two roots of the equation x^4-20x^3+kx^2+590x-1992=0 is 24. Find k

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Solve 4x³ - 24x² + 23x + 18 = 0, whose roots are in A.P.@EAG

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Solve the equations:x^{4} - 2x^{3} - 21x^{2} + 22x + 40 = 0, the roots being in arithmetical progression.

Solve 4x³ - 24x² + 23x + 18 = 0, whose roots are in A.P.@EAG

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.

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