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If f(x) is a monic quartic polynomial such that f(-1) = -1, f(2) = -4, f(3) = -9, and f(4) = -16, find f(1).

 Apr 5, 2022
 #1
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\(f(x)=x^4+bx^3+cx^2+d\qquad \\ find\;\;f(1)\\ f(1)=1+b+c+d\\~\\ \\f(-1)=1-b+c+d=-1\\ c+d=-2+b\\ so\\ f(1)=1+b+-2+b\\ f(1)=-1+2b\\ \)

From there i found expressions for  f(2),   f(3)   and  f(4)    and solved simulatneously to find b

 

I'll let you try it from there.

 

 

 

LaTex:

f(x)=x^4+bx^3+cx^2+d\qquad  \\
find\;\;f(1)\\
f(1)=1+b+c+d\\~\\
\\f(-1)=1-b+c+d=-1\\
c+d=-2+b\\
so\\
f(1)=1+b+-2+b\\
f(1)=-1+2b\\

 Apr 5, 2022

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