Question

Find solution to interpolation, and what exact conditions is deg (q) = 2?

& Find solution to the interpolation problem of finding a polynomial 9x with deg (9) £2 and such that: 9(x) = Yo 4.X) PY q (x) = Yi with Xo LX. Under what exact conditions is deg (q) = 2?

Answer 1

tet as to) = a + bn & Cu² using given condition qulmo) = a (n) = 4, Q1" (Mi) = 42 Yo = a (no)= = a + b + (10² 4, = a('ser) = a + b 4, +(4,2- 4' - 21(M) = b +QCM, ) my b = 4, -20% in D & S 0 use 13 You = in at(Y,'- 2011) , + (11,2 4, = aty, n-0x2 Y, 4, 4, = a-cut Yo = a +(4, -204) Moot Chor Yo-Y,'rg = a +(1²-2010) -u? 4,-4,' so²=20,00 40 -4;'vo 4, -4,'s, 0 (Mor)? 4. c7'vo no <1, =) do fr ca Horu, je 2? (40-4, I do) Trou; j2 4,-4,',c a = 4-4'4 + 2,21% 4, Ho) [2)=( 7 JC) به tant Com Yo-Y,'no = a こ ol Ro

we have a = (4,-4, 'xs) (mor wo) ? + x4 ( 40 –Y'40) -6 Usis b 4,'(wg - 2)2- 2149-4'80), C = it (%o54'wo) ro =0 thon (nor ",)2 a Mo - Me )? (Yo - Yllo) Mon 8,32 = Y. 4, =costant Mo =0 c= al (1) # of form atbu , where a, b 6,7 the degree of a (n) <2 Yo 4, 'W. than 8M) if of foom atbu toe where are If Yo a, b, c are gluen: In 6 ,7,8 dea q=2