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Answer 1 · 2017-10-24T07:47:48

#a=3,b=-4#

if we have #(x-a)^2 as a divisor

then

#ax^4+bx^3+1=Q(x)(x-1)^2---(1)#

#x=1#

#a+b+1=0=>a+b=-1---(2)#

differentiate #(1)#

#4ax^3+3bx^2=Q'(x)(x-1)^2+2Q(x)(x-1)#

#x=1#

#4a+3b=0---(3)#

#(2)xx4#

#4a+4b=-4---(2a)#

#4a+3b=0---(3)#

subtract

#b=-4#

#a+b=-1=>a+ -4=-1#

#a=3#

mental check for consistency in #(3)sqrt#

#a=3,b=-4#