- #1

chwala

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## Homework Statement:

- The polynomial ##4x^4+Ax^2+11x+b## where ##a## and ##b## are constants, is denoted by ##p(x)##. It is given that ##p(x)## is divisible by ##x^2-x+2##. Find the values of ##a## and ##b##

## Relevant Equations:

- factor theorem

##4x^4+Ax^2+11x+b##≡##(x^2-x+2)(ax^2+mx+d)##

≡##ax^4+(m-a)x^3+(d-m+2a)x^2+(2m-d)x+2d##

##a=4##

##m-a=0, m=4##

##d-m+2a=A##

##2m-d=11##

##2d=b##

##A=1##, ## B=-6 ## is that correct?

≡##ax^4+(m-a)x^3+(d-m+2a)x^2+(2m-d)x+2d##

##a=4##

##m-a=0, m=4##

##d-m+2a=A##

##2m-d=11##

##2d=b##

##A=1##, ## B=-6 ## is that correct?