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Question

2x^4+9x^3-16x-72=0

Answer 1

2x⁴ + 9x³ - 16x - 72 = 0

 

x³(2x + 9) - 8(2x + 9) = 0

 

(2x + 9)(x³ - 1) = 0

 

(2x + 9)(x - 2)(x² + 2x + 4) = 0

 

Setting each factor to 0 and solving (quadratic formula for the last one) gives:

 

x ∈ {-9/2 , 1 , -1+i√3 , -1-i√3 }