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p(x)=x^4+5x^3+4x^2-3x^2+9=(x-k)^2(ax^2+bx+c) where k is an integer and a,b,c are constants.Find the value of 5a-7b+8c

p(x)=x^4+5x^3+4x^2-3x^2+9=(x-k)^2(ax^2+bx+c) where k is an integer and a,b,c are constants.Find the value of 5a-7b+8c

Grade:12th pass

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,

at x=0
9=(k^2)c =>c=1 , k=3
at x=1
16=4(a+b+1) =>a+b =3
at x=2
53=4a+2b+1 =>4a+2b=52
a=23 & b=-20
=>5*46-7*(-20)+8=378

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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