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))

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