R9alphabeta[x_]=x^9+(-9s)*x^8+a7*x^7+a6*x^6+a5 x^5+a4 x^4+a3 x^3+a2 x^2+a1 x+a0;
1/143360 (143360 x^9+6000 \[Alpha]^3-2016 \[Alpha]^5-1863 \[Alpha]^7-2240 \[Beta]-16080 \[Alpha]^2 \[Beta]-13932 \[Alpha]^4 \[Beta]+9891 \[Alpha]^6 \[Beta]+14160 \[Alpha] \[Beta]^2+76464 \[Alpha]^3 \[Beta]^2+2877 \[Alpha]^5 \[Beta]^2-1863 \[Alpha]^7 \[Beta]^2+29520 \[Beta]^3-14328 \[Alpha]^2 \[Beta]^3-114465 \[Alpha]^4 \[Beta]^3+4851 \[Alpha]^6 \[Beta]^3-134928 \[Alpha] \[Beta]^4-16629 \[Alpha]^3 \[Beta]^4+42357 \[Alpha]^5 \[Beta]^4-32220 \[Beta]^5+177081 \[Alpha]^2 \[Beta]^5+24627 \[Alpha]^4 \[Beta]^5+92895 \[Alpha] \[Beta]^6-62565 \[Alpha]^3 \[Beta]^6+11493 \[Beta]^7-61887 \[Alpha]^2 \[Beta]^7-14889 \[Alpha] \[Beta]^8-2311 \[Beta]^9-53760 x^6 (\[Alpha]-\[Beta])^2 (\[Alpha]+\[Beta])-68024448 s^7 (-1+2 x^2-\[Beta]^2)-80640 x^7 (4+\[Alpha]^2-2 \[Alpha] \[Beta]+\[Beta]^2)+2016 x^4 (\[Alpha]-\[Beta])^2 (52 \[Alpha]+\[Alpha]^3+52 \[Beta]-33 \[Alpha]^2 \[Beta]-33 \[Alpha] \[Beta]^2+\[Beta]^3)+26453952 s^6 (-4 x+4 x^3+6 x^2 (\[Alpha]+\[Beta])-3 \[Alpha] (1+\[Beta]^2)-\[Beta] (1+5 \[Beta]^2))-5040 x^5 (-48+3 \[Alpha]^4+12 \[Alpha]^3 \[Beta]-32 \[Beta]^2+3 \[Beta]^4+4 \[Alpha] \[Beta] (16+3 \[Beta]^2)-2 \[Alpha]^2 (16+15 \[Beta]^2))-734832 s^5 (20+96 x^4+95 \[Beta]^2-141 \[Beta]^4-120 x (\[Alpha]+\[Beta])+120 x^3 (\[Alpha]+\[Beta])-33 \[Alpha]^2 (1+\[Beta]^2)+2 x^2 (-68+33 \[Alpha]^2+134 \[Alpha] \[Beta]+33 \[Beta]^2)-2 \[Alpha] \[Beta] (37+97 \[Beta]^2))-280 x (-16+18 \[Alpha]^6-141 \[Alpha]^5 \[Beta]-72 \[Beta]^2+63 \[Beta]^4+18 \[Beta]^6+\[Alpha]^4 (63-78 \[Beta]^2)+6 \[Alpha]^3 \[Beta] (24+67 \[Beta]^2)-6 \[Alpha]^2 (12+69 \[Beta]^2+13 \[Beta]^4)-3 \[Alpha] \[Beta] (-48-48 \[Beta]^2+47 \[Beta]^4))+18 x^2 (\[Alpha]-\[Beta])^2 (207 \[Alpha]^5-405 \[Alpha]^4 \[Beta]+\[Alpha]^3 (112-3642 \[Beta]^2)+\[Alpha]^2 (6672 \[Beta]-3642 \[Beta]^3)+\[Alpha] (-3504+6672 \[Beta]^2-405 \[Beta]^4)+\[Beta] (-3504+112 \[Beta]^2+207 \[Beta]^4))+840 x^3 (-80+6 \[Alpha]^6-47 \[Alpha]^5 \[Beta]-120 \[Beta]^2+39 \[Beta]^4+6 \[Beta]^6+\[Alpha]^4 (39-26 \[Beta]^2)+2 \[Alpha]^3 \[Beta] (60+67 \[Beta]^2)-2 \[Alpha]^2 (60+159 \[Beta]^2+13 \[Beta]^4)+\[Alpha] (240 \[Beta]+120 \[Beta]^3-47 \[Beta]^5))+408240 s^4 (96 x^5+96 x^4 (\[Alpha]+\[Beta])+9 \[Alpha]^3 (1+\[Beta]^2)+2 x^3 (-76+15 \[Alpha]^2+106 \[Alpha] \[Beta]+15 \[Beta]^2)-2 x (-28+15 \[Alpha]^2+106 \[Alpha] \[Beta]+15 \[Beta]^2)-6 \[Alpha]^2 \[Beta] (13+18 \[Beta]^2)+\[Alpha] (24+85 \[Beta]^2-247 \[Beta]^4)-2 \[Beta] (2-86 \[Beta]^2+51 \[Beta]^4)-6 x^2 (3 \[Alpha]^3-31 \[Alpha]^2 \[Beta]+\[Alpha] (24-31 \[Beta]^2)+3 \[Beta] (8+\[Beta]^2)))-4536 s^3 (-232+3840 x^6-2518 \[Beta]^2+5859 \[Beta]^4-1995 \[Beta]^6+2880 x^5 (\[Alpha]+\[Beta])+6720 x^4 (-1+\[Alpha] \[Beta])+675 \[Alpha]^4 (1+\[Beta]^2)+60 \[Alpha]^3 \[Beta] (-20+3 \[Beta]^2)+60 x (32 \[Alpha]+23 \[Alpha]^3+32 \[Beta]-83 \[Alpha]^2 \[Beta]-83 \[Alpha] \[Beta]^2+23 \[Beta]^3)-60 x^3 (80 \[Alpha]+23 \[Alpha]^3+80 \[Beta]-83 \[Alpha]^2 \[Beta]-83 \[Alpha] \[Beta]^2+23 \[Beta]^3)-2 \[Alpha]^2 (-57+719 \[Beta]^2+3266 \[Beta]^4)+\[Alpha] (836 \[Beta]+9536 \[Beta]^3-7800 \[Beta]^5)-2 x^2 (-1672+675 \[Alpha]^4-510 \[Alpha]^3 \[Beta]+114 \[Beta]^2+675 \[Beta]^4+\[Alpha]^2 (114-4042 \[Beta]^2)+\[Alpha] (5156 \[Beta]-510 \[Beta]^3)))+504 s^2 (11520 x^7+688 \[Beta]-9868 \[Beta]^3+9357 \[Beta]^5-2061 \[Beta]^7+5760 x^6 (\[Alpha]+\[Beta])+864 \[Alpha]^5 (1+\[Beta]^2)-960 x^5 (23+3 \[Alpha]^2-17 \[Alpha] \[Beta]+3 \[Beta]^2)+45 \[Alpha]^4 \[Beta] (25+103 \[Beta]^2)-240 x^4 (44 \[Alpha]+21 \[Alpha]^3+44 \[Beta]-41 \[Alpha]^2 \[Beta]-41 \[Alpha] \[Beta]^2+21 \[Beta]^3)-30 \[Alpha]^3 (45+338 \[Beta]^2+91 \[Beta]^4)+\[Alpha]^2 (3864 \[Beta]+8974 \[Beta]^3-18154 \[Beta]^5)-2 \[Alpha] (228+2683 \[Beta]^2-14722 \[Beta]^4+6285 \[Beta]^6)-2 x^3 (-6424+1755 \[Alpha]^4+510 \[Alpha]^3 \[Beta]-2202 \[Beta]^2+1755 \[Beta]^4+2 \[Alpha] \[Beta] (6886+255 \[Beta]^2)-2 \[Alpha]^2 (1101+4457 \[Beta]^2))+2 x (-1144+1755 \[Alpha]^4+510 \[Alpha]^3 \[Beta]-762 \[Beta]^2+1755 \[Beta]^4-2 \[Alpha]^2 (381+4457 \[Beta]^2)+\[Alpha] (5612 \[Beta]+510 \[Beta]^3))-12 x^2 (144 \[Alpha]^5+480 \[Alpha]^4 \[Beta]-15 \[Alpha]^3 (43+64 \[Beta]^2)+\[Alpha]^2 (1337 \[Beta]-960 \[Beta]^3)+\[Beta] (-476-645 \[Beta]^2+144 \[Beta]^4)+\[Alpha] (-476+1337 \[Beta]^2+480 \[Beta]^4)))-12 s (107520 x^8+26880 x^7 (\[Alpha]+\[Beta])+126 \[Alpha]^6 (1+\[Beta]^2)-2240 x^6 (100+21 \[Alpha]^2-58 \[Alpha] \[Beta]+21 \[Beta]^2)+126 \[Alpha]^5 \[Beta] (137+190 \[Beta]^2)-6720 x^5 (8 \[Alpha]+7 \[Alpha]^3+8 \[Beta]-9 \[Alpha]^2 \[Beta]-9 \[Alpha] \[Beta]^2+7 \[Beta]^3)+7 \[Alpha]^4 (-1317-6686 \[Beta]^2+5981 \[Beta]^4)-4 \[Alpha]^3 \[Beta] (-2825+20207 \[Beta]^2+12483 \[Beta]^4)-6 \[Alpha]^2 (-548-6499 \[Beta]^2-26041 \[Beta]^4+17724 \[Beta]^6)-2 \[Alpha] \[Beta] (3608+56058 \[Beta]^2-85331 \[Beta]^4+21952 \[Beta]^6)+5 (80+4680 \[Beta]^2-12179 \[Beta]^4+6286 \[Beta]^6-1029 \[Beta]^8)-84 x^4 (-1776+275 \[Alpha]^4+380 \[Alpha]^3 \[Beta]-1008 \[Beta]^2+275 \[Beta]^4-18 \[Alpha]^2 (56+87 \[Beta]^2)+4 \[Alpha] \[Beta] (712+95 \[Beta]^2))+14 x (477 \[Alpha]^5+4025 \[Alpha]^4 \[Beta]-6 \[Alpha]^2 \[Beta] (-566+857 \[Beta]^2)-2 \[Alpha]^3 (1258+2571 \[Beta]^2)+\[Beta] (-480-2516 \[Beta]^2+477 \[Beta]^4)+\[Alpha] (-480+3396 \[Beta]^2+4025 \[Beta]^4))-14 x^3 (477 \[Alpha]^5+4025 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (2938+2571 \[Beta]^2)+\[Alpha]^2 (7716 \[Beta]-5142 \[Beta]^3)+\[Beta] (-2400-5876 \[Beta]^2+477 \[Beta]^4)+\[Alpha] (-2400+7716 \[Beta]^2+4025 \[Beta]^4))-6 x^2 (5584+42 \[Alpha]^6+6867 \[Alpha]^5 \[Beta]+7368 \[Beta]^2-6923 \[Beta]^4+42 \[Beta]^6+7 \[Alpha]^4 (-989+102 \[Beta]^2)-58 \[Alpha]^3 \[Beta] (128+307 \[Beta]^2)+6 \[Alpha]^2 (1228+5913 \[Beta]^2+119 \[Beta]^4)+\[Alpha] \[Beta] (-21744-7424 \[Beta]^2+6867 \[Beta]^4))))
a0=Coefficient[R9alphabeta[x],x,0]//Simplify
1/143360 (-2240 \[Beta]+29520 \[Beta]^3-32220 \[Beta]^5+11493 \[Beta]^7-2311 \[Beta]^9+68024448 s^7 (1+\[Beta]^2)-1863 \[Alpha]^7 (1+\[Beta]^2)+63 \[Alpha]^6 \[Beta] (157+77 \[Beta]^2)+21 \[Alpha]^5 (-96+137 \[Beta]^2+2017 \[Beta]^4)+3 \[Alpha]^4 \[Beta] (-4644-38155 \[Beta]^2+8209 \[Beta]^4)+\[Alpha]^3 (6000+76464 \[Beta]^2-16629 \[Beta]^4-62565 \[Beta]^6)-3 \[Alpha] \[Beta]^2 (-4720+44976 \[Beta]^2-30965 \[Beta]^4+4963 \[Beta]^6)-3 \[Alpha]^2 \[Beta] (5360+4776 \[Beta]^2-59027 \[Beta]^4+20629 \[Beta]^6)-26453952 s^6 (\[Beta]+5 \[Beta]^3+3 \[Alpha] (1+\[Beta]^2))+734832 s^5 (-20-95 \[Beta]^2+141 \[Beta]^4+33 \[Alpha]^2 (1+\[Beta]^2)+2 \[Alpha] \[Beta] (37+97 \[Beta]^2))+408240 s^4 (9 \[Alpha]^3 (1+\[Beta]^2)-6 \[Alpha]^2 \[Beta] (13+18 \[Beta]^2)+\[Alpha] (24+85 \[Beta]^2-247 \[Beta]^4)-2 \[Beta] (2-86 \[Beta]^2+51 \[Beta]^4))-4536 s^3 (-232-2518 \[Beta]^2+5859 \[Beta]^4-1995 \[Beta]^6+675 \[Alpha]^4 (1+\[Beta]^2)+60 \[Alpha]^3 \[Beta] (-20+3 \[Beta]^2)-2 \[Alpha]^2 (-57+719 \[Beta]^2+3266 \[Beta]^4)+\[Alpha] (836 \[Beta]+9536 \[Beta]^3-7800 \[Beta]^5))+504 s^2 (688 \[Beta]-9868 \[Beta]^3+9357 \[Beta]^5-2061 \[Beta]^7+864 \[Alpha]^5 (1+\[Beta]^2)+45 \[Alpha]^4 \[Beta] (25+103 \[Beta]^2)-30 \[Alpha]^3 (45+338 \[Beta]^2+91 \[Beta]^4)+\[Alpha]^2 (3864 \[Beta]+8974 \[Beta]^3-18154 \[Beta]^5)-2 \[Alpha] (228+2683 \[Beta]^2-14722 \[Beta]^4+6285 \[Beta]^6))-12 s (126 \[Alpha]^6 (1+\[Beta]^2)+126 \[Alpha]^5 \[Beta] (137+190 \[Beta]^2)+7 \[Alpha]^4 (-1317-6686 \[Beta]^2+5981 \[Beta]^4)-4 \[Alpha]^3 \[Beta] (-2825+20207 \[Beta]^2+12483 \[Beta]^4)-6 \[Alpha]^2 (-548-6499 \[Beta]^2-26041 \[Beta]^4+17724 \[Beta]^6)-2 \[Alpha] \[Beta] (3608+56058 \[Beta]^2-85331 \[Beta]^4+21952 \[Beta]^6)+5 (80+4680 \[Beta]^2-12179 \[Beta]^4+6286 \[Beta]^6-1029 \[Beta]^8)))
a1=Coefficient[R9alphabeta[x],x,1]//Simplify
1/2560 (-1889568 s^6+1574640 s^5 (\[Alpha]+\[Beta])-14580 s^4 (-28+15 \[Alpha]^2+106 \[Alpha] \[Beta]+15 \[Beta]^2)-4860 s^3 (32 \[Alpha]+23 \[Alpha]^3+32 \[Beta]-83 \[Alpha]^2 \[Beta]-83 \[Alpha] \[Beta]^2+23 \[Beta]^3)+18 s^2 (-1144+1755 \[Alpha]^4+510 \[Alpha]^3 \[Beta]-762 \[Beta]^2+1755 \[Beta]^4-2 \[Alpha]^2 (381+4457 \[Beta]^2)+\[Alpha] (5612 \[Beta]+510 \[Beta]^3))-5 (-16+18 \[Alpha]^6-141 \[Alpha]^5 \[Beta]-72 \[Beta]^2+63 \[Beta]^4+18 \[Beta]^6+\[Alpha]^4 (63-78 \[Beta]^2)+6 \[Alpha]^3 \[Beta] (24+67 \[Beta]^2)-6 \[Alpha]^2 (12+69 \[Beta]^2+13 \[Beta]^4)-3 \[Alpha] \[Beta] (-48-48 \[Beta]^2+47 \[Beta]^4))-3 s (477 \[Alpha]^5+4025 \[Alpha]^4 \[Beta]-6 \[Alpha]^2 \[Beta] (-566+857 \[Beta]^2)-2 \[Alpha]^3 (1258+2571 \[Beta]^2)+\[Beta] (-480-2516 \[Beta]^2+477 \[Beta]^4)+\[Alpha] (-480+3396 \[Beta]^2+4025 \[Beta]^4)))
a2=Coefficient[R9alphabeta[x],x,2]//Simplify
-1/71680 9 (7558272 s^7-8817984 s^6 (\[Alpha]+\[Beta])+81648 s^5 (-68+33 \[Alpha]^2+134 \[Alpha] \[Beta]+33 \[Beta]^2)+136080 s^4 (3 \[Alpha]^3-31 \[Alpha]^2 \[Beta]+\[Alpha] (24-31 \[Beta]^2)+3 \[Beta] (8+\[Beta]^2))-504 s^3 (-1672+675 \[Alpha]^4-510 \[Alpha]^3 \[Beta]+114 \[Beta]^2+675 \[Beta]^4+\[Alpha]^2 (114-4042 \[Beta]^2)+\[Alpha] (5156 \[Beta]-510 \[Beta]^3))-(\[Alpha]-\[Beta])^2 (207 \[Alpha]^5-405 \[Alpha]^4 \[Beta]+\[Alpha]^3 (112-3642 \[Beta]^2)+\[Alpha]^2 (6672 \[Beta]-3642 \[Beta]^3)+\[Alpha] (-3504+6672 \[Beta]^2-405 \[Beta]^4)+\[Beta] (-3504+112 \[Beta]^2+207 \[Beta]^4))+336 s^2 (144 \[Alpha]^5+480 \[Alpha]^4 \[Beta]-15 \[Alpha]^3 (43+64 \[Beta]^2)+\[Alpha]^2 (1337 \[Beta]-960 \[Beta]^3)+\[Beta] (-476-645 \[Beta]^2+144 \[Beta]^4)+\[Alpha] (-476+1337 \[Beta]^2+480 \[Beta]^4))-4 s (5584+42 \[Alpha]^6+6867 \[Alpha]^5 \[Beta]+7368 \[Beta]^2-6923 \[Beta]^4+42 \[Beta]^6+7 \[Alpha]^4 (-989+102 \[Beta]^2)-58 \[Alpha]^3 \[Beta] (128+307 \[Beta]^2)+6 \[Alpha]^2 (1228+5913 \[Beta]^2+119 \[Beta]^4)+\[Alpha] \[Beta] (-21744-7424 \[Beta]^2+6867 \[Beta]^4)))
a3=Coefficient[R9alphabeta[x],x,3]//Simplify
1/2560 3 (629856 s^6-524880 s^5 (\[Alpha]+\[Beta])+4860 s^4 (-76+15 \[Alpha]^2+106 \[Alpha] \[Beta]+15 \[Beta]^2)+1620 s^3 (80 \[Alpha]+23 \[Alpha]^3+80 \[Beta]-83 \[Alpha]^2 \[Beta]-83 \[Alpha] \[Beta]^2+23 \[Beta]^3)-6 s^2 (-6424+1755 \[Alpha]^4+510 \[Alpha]^3 \[Beta]-2202 \[Beta]^2+1755 \[Beta]^4+2 \[Alpha] \[Beta] (6886+255 \[Beta]^2)-2 \[Alpha]^2 (1101+4457 \[Beta]^2))+s (477 \[Alpha]^5+4025 \[Alpha]^4 \[Beta]-2 \[Alpha]^3 (2938+2571 \[Beta]^2)+\[Alpha]^2 (7716 \[Beta]-5142 \[Beta]^3)+\[Beta] (-2400-5876 \[Beta]^2+477 \[Beta]^4)+\[Alpha] (-2400+7716 \[Beta]^2+4025 \[Beta]^4))+5 (-80+6 \[Alpha]^6-47 \[Alpha]^5 \[Beta]-120 \[Beta]^2+39 \[Beta]^4+6 \[Beta]^6+\[Alpha]^4 (39-26 \[Beta]^2)+2 \[Alpha]^3 \[Beta] (60+67 \[Beta]^2)-2 \[Alpha]^2 (60+159 \[Beta]^2+13 \[Beta]^4)+\[Alpha] (240 \[Beta]+120 \[Beta]^3-47 \[Beta]^5)))
a4=Coefficient[R9alphabeta[x],x,4]//Simplify
-1/1280 9 (69984 s^5-38880 s^4 (\[Alpha]+\[Beta])+30240 s^3 (-1+\[Alpha] \[Beta])-2 (\[Alpha]-\[Beta])^2 (52 \[Alpha]+\[Alpha]^3+52 \[Beta]-33 \[Alpha]^2 \[Beta]-33 \[Alpha] \[Beta]^2+\[Beta]^3)+120 s^2 (44 \[Alpha]+21 \[Alpha]^3+44 \[Beta]-41 \[Alpha]^2 \[Beta]-41 \[Alpha] \[Beta]^2+21 \[Beta]^3)+s (1776-275 \[Alpha]^4-380 \[Alpha]^3 \[Beta]+1008 \[Beta]^2-275 \[Beta]^4+18 \[Alpha]^2 (56+87 \[Beta]^2)-4 \[Alpha] \[Beta] (712+95 \[Beta]^2)))
a5=Coefficient[R9alphabeta[x],x,5]//Simplify
9/256 (48+7776 s^4-3 \[Alpha]^4-12 \[Alpha]^3 \[Beta]+32 \[Beta]^2-3 \[Beta]^4-2592 s^3 (\[Alpha]+\[Beta])-4 \[Alpha] \[Beta] (16+3 \[Beta]^2)-96 s^2 (23+3 \[Alpha]^2-17 \[Alpha] \[Beta]+3 \[Beta]^2)+\[Alpha]^2 (32+30 \[Beta]^2)+16 s (8 \[Alpha]+7 \[Alpha]^3+8 \[Beta]-9 \[Alpha]^2 \[Beta]-9 \[Alpha] \[Beta]^2+7 \[Beta]^3))
a6=Coefficient[R9alphabeta[x],x,6]//Simplify
-(3/16) (648 s^3-108 s^2 (\[Alpha]+\[Beta])+2 (\[Alpha]-\[Beta])^2 (\[Alpha]+\[Beta])-s (100+21 \[Alpha]^2-58 \[Alpha] \[Beta]+21 \[Beta]^2))
a7=Coefficient[R9alphabeta[x],x,7]//Simplify
9/16 (-4+72 s^2-\[Alpha]^2+2 \[Alpha] \[Beta]-\[Beta]^2-4 s (\[Alpha]+\[Beta]))
a8=Coefficient[R9alphabeta[x],x,8]//Simplify
-9 s
a9=Coefficient[R9alphabeta[x],x,9]//Simplify
1