Solve the following equation in the complex number system. Please show all of your work.5x^5 +32x^4 -5x -32= 0

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rcmath | High School Teacher | (Level 1) Associate Educator

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We start by factoring the polynomial

`x^4(5x+32)-(5x+32)=0 =>`

`(5x+32)(x^4-1)=0`

`(5x+32)(x^2-1)(x^2+1)=0 =>`

`(5x+32)(x-1)(x+1)(x^2+1)=0`

`5x+32=0 => x=-32/5`

`or x-1=0 => x=1`

`or x+1=0 => x=-1`

`or x^2+1=0 => x^2=-1 => x=i or -i`` `

Hence your solutions are `-32/5 or+-1 or +-i`

 

 

 

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