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p-x-x-4-ax-3-bx-2-cx-d-if-p-1-10-p-2-20-and-p-3-30-find-p-12-p-8-10-

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Question Number 103832 by bemath last updated on 17/Jul/20
p(x) = x^4 +ax^3 +bx^2 +cx +d if p(1)=10,p(2)=20 and p(3)=30 . find ((p(12)+p(−8))/(10))
p(x)=x4+ax3+bx2+cx+difp(1)=10,p(2)=20andp(3)=30.findp(12)+p(−8)10
Answered by floor(10²Eta[1]) last updated on 17/Jul/20
p(x)=(x−1)(x−2)(x−3)(x−x_4 )+10x p(12)=11.10.9(12−x_4 )+120 p(−8)=(−9)(−10)(−11)(−8−x_4 )−80 ((p(12)+p(−8))/(10))=99(12−x_4 )+12−99(−8−x_4 )−8 =99[(12−x_4 )−(−8−x_4 )]+4=99.20+4=1984
p(x)=(x−1)(x−2)(x−3)(x−x4)+10xp(12)=11.10.9(12−x4)+120p(−8)=(−9)(−10)(−11)(−8−x4)−80p(12)+p(−8)10=99(12−x4)+12−99(−8−x4)−8=99[(12−x4)−(−8−x4)]+4=99.20+4=1984

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