If x^2+5 x+7 (x-3)^3 + A (x-3) + [ B (x-3)^2 + C (x-3)^3 . , then the equation of the line having slope A and passing through the point (B, C) is

Step-by-step solution

We have, aligned & x^2+5 x+7 (x-3)^3 = A x-3 + B (x-3)^2 + C (x-3)^3 x^2+5 x+7 & =A(x-3)^2+B(x-3)+C aligned Put x=3 in Eq. (i), we get array rlrl 9+15+7 & =C & & C & =31 array Put x=0 in Eq. (i), we get aligned & 7=9 A-3 B+31 & 9 A-3 B=-24 & 3 A-B=-8 & aligned Put x=1 in Eq. (i), we get aligned & 1+5+7=4 A-2 B+31 & 13=4 A-2 B+31 & 4 A-2 B=-18 & 2 A-B=-9 & On solving Eqs. (ii) and (iii), we get & A=1 & and & B=11 & aligned ∴ Equation of line having slope A and pass ing through the points (B, C) is y − 31 = 1(x − 11)