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Question Number 11628 by uni last updated on 29/Mar/17
p(x−1)+p(x+1)=4x^2 −2x+10 p(x)=?
p(x−1)+p(x+1)=4x2−2x+10p(x)=?
Answered by sandy_suhendra last updated on 29/Mar/17
let p(x)=ax^2 +bx+c p(x−1)=a(x−1)^2 +b(x−1)+c =a(x^2 −2x+1)+b(x−1)+c p(x+1)=a(x+1)^2 +b(x+1)+c =a(x^2 +2x+1)+b(x+1)+c coefisien of x^2 ⇒a+a=4⇒a=2 coefisien of x⇒−2a+b+2a+b=−2⇒b=−1 constant⇒a−b+c+a+b+c=10 2a+2c=10⇒4+2c=10⇒c=3 p(x)=2x^2 −x+3
letp(x)=ax2+bx+cp(x−1)=a(x−1)2+b(x−1)+c=a(x2−2x+1)+b(x−1)+cp(x+1)=a(x+1)2+b(x+1)+c=a(x2+2x+1)+b(x+1)+ccoefisienofx2⇒a+a=4⇒a=2coefisienofx⇒−2a+b+2a+b=−2⇒b=−1constant⇒a−b+c+a+b+c=102a+2c=10⇒4+2c=10⇒c=3p(x)=2x2−x+3

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