x^4-8x^2+8x+6=0 each diminished by 2
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Given equation is x4−5x3+7x2−17x+11=0
Replacing x→x+2, we get
(x+2)4−5(x+2)3+7(x+2)2−17(x+2)+11=0
⇒(x+2)2(x+2)2−5(x+2)3+7(x2+4x+4)−17x−34+11=0
⇒x4+3x3+x2−17x−19=0
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