Question

2 Find the solution to the interpolation problem of finding a polynomial qr) with degy and such that 01:1) = yi and with B. Under what exact conditions is deg(q) = 2

Answer 1

Given that a The interpolation problem of finding polynomial qcx) with deq (2) <2 let us consider, 900) at butcx² conditions are, 2010) - Yo q cw) = 4 q' (x1) = 4' Yo = q (uo Yo = atbrot cro Y = 200) atbaitan Ego 16 b+Qcxl Yi → byl-20x

in Now using zga @ ear Y, = a + Cyi-804) at came & -atxix, - car? >4, yun a car eqh in Yo = at cei-acx not (10² Yo-Yino at (2-21 ) C -21 Yi-Yixi Yo - 8/10 no-ann .] -II-CE 2 Yiying Yo-yo do 0 (1-21) Thertore, lo y → 70 Now to calculate the carb values

> V Co Yo-Y, 20 Cho-2,22 a (yo-ylio) – 4, 4, 21 lo-n) 2 a= Y.-yint - Cro-vino) 010-42 and we halce, V a=(4,-4) (90-21 )"+ Yo-Yiro) (on)2 be yi (12-2)²- a (yo-kinox, (Xo-2) ² ly m kt) (Yo-y!26) (lon)? vity it no=yo =0 Y = constant -o (4 - 6100) Then, c=0

å 902) is of yorm latba Where a b are VO $ vii degree of 902)<a it Yo t li no Hence, 962) i ot form atbatca² where, a, b, c are v 0 deq deq qza Thank you