# Difficulty solving a polynomial.

``````k1 = 0.01;
k2 - 0.01;
k3 = 0.01;
R = {{-317074. - 3255.08 k1 - 6510.16 k2 + 39.25 b ^ 2, -241517. -
4593.15 k1 - 5295.88 k2 + 29.897 b ^ 2, -7.25817 * 10 ^ -7 +
4603.38 k1 - 3.69363 * 10 ^ -9 k2 - 1.12278 * 10 ^ -11 b ^ 2, -10161.8 -
409,588 k1 + 0.397884 k2 + 1.25525 b ^ 2,
126793. - 9.34595 * 10 ^ -9 k1 + 2780.26 k2 - 15.6955 b ^ 2,
64244.2 - 1.90887 * 10 ^ -8 k1 + 2574.91 k2 - 7.95115 b ^ 2, -10781.2 -
1.8725 * 10 ^ -9 k1 + 0.292511 k2 + 1.33767 b ^ 2, -2.07898 -
7.30152 * 10 ^ -12 k1 + 0.00825368 k2 + 0.0000109055 b ^ 2, -76688.6 +
3977.98 k1 - 7007.88 k2 + 9.49819 b ^ 2, -9234.46 - 185.204 k1 +
0.0237841 k2 + 1.14341 b ^ 2,
22001. - 2.12083 * 10 ^ -8 k1 + 2009.06 k2 - 2.72346 b ^ 2,
65.6162 - 8.03025 * 10 ^ -10 k1 - 0.610304 k2 +
0.00145184 b ^ 2}, {-241517. - 4593.15 k1 - 5295.88 k2 +
29.897 b ^ 2, -1.49882 * 10 ^ 6 - 6481.27 k1 - 4308.09 k2 +
32.4507 b ^ 2,
2.50722 * 10 ^ 6 + 6495.7 k1 - 3.00469 * 10 ^ -9 k2 -
19.3977 b ^ 2, -81891.2 - 577.959 k1 + 0.32367 k2 +
1.77261 b ^ 2, -522099. - 1.31878 * 10 ^ -8 k1 + 2261.69 k2 -
6.9699 b ^ 2,
295696. - 2.69355 * 10 ^ -8 k1 + 2094.64 k2 - 6.40372 b ^ 2,
151362. - 2.64224 * 10 ^ -9 k1 + 0.237952 k2 +
0.0314201 b ^ 2, -5.60481 - 1.0303 * 10 ^ -11 k1 + 0.0067142 k2 +
0.0000107143 b ^ 2,
107.591 + 5613.22 k1 - 5700.77 k2 - 0.00126411 b ^ 2,
26886.8 - 261.336 k1 + 0.0193479 k2 + 0.821086 b ^ 2,
631401. - 2.99265 * 10 ^ -8 k1 + 1634.33 k2 - 5.02847 b ^ 2, -638.944 -
1.13313 * 10 ^ -9 k1 - 0.49647 k2 +
0.00477873 b ^ 2}, {-7.25817 * 10 ^ -7 + 4603.38 k1 -
3.69363 * 10 ^ -9 k2 - 1.12278 * 10 ^ -11 b ^ 2,
2.50722 * 10 ^ 6 + 6495.7 k1 - 3.00469 * 10 ^ -9 k2 -
19.3977 b ^ 2, -5.07318 * 10 ^ 6 - 6510.16 k1 - 2.09563 * 10 ^ -21 k2 +
39.25 b ^ 2,
227898. + 579.246 k1 + 2.25745 * 10 ^ -13 k2 - 1.76248 b ^ 2,
1.31625 * 10 ^ 6 + 1.32172 * 10 ^ -8 k1 + 1.57742 * 10 ^ -9 k2 -
10.1835 b ^ 2, -31.4777 + 2.69954 * 10 ^ -8 k1 + 1.46091 * 10 ^ -9 k2 +
0.000244454 b ^ 2, -243037. + 2.64812 * 10 ^ -9 k1 +
1.6596 * 10 ^ -13 k2 + 1.88102 b ^ 2,
13.4875 + 1.03259 * 10 ^ -11 k1 + 4.68284 * 10 ^ -15 k2 -
0.0000171871 b ^ 2, -2.29463 * 10 ^ 6 - 5625.71 k1 -
3.97602 * 10 ^ -9 k2 + 17.7514 b ^ 2,
29.4428 + 261.918 k1 + 1.34942 * 10 ^ -14 k2 -
0.00009334 b ^ 2, -657764. + 2.99931 * 10 ^ -8 k1 + 1.13987 * 10 ^ -9 k2 +
5.08896 b ^ 2,
754.94 + 1.13565 * 10 ^ -9 k1 - 3.46264 * 10 ^ -13 k2 +
0.000759213 b ^ 2}, {-10161.8 - 409.588 k1 + 0.397884 k2 +
1.25525 b ^ 2, -81891.2 - 577.959 k1 + 0.32367 k2 + 1.77261 b ^ 2,
227898. + 579.246 k1 + 2.25745 * 10 ^ -13 k2 -
1.76248 b ^ 2, -33454.3 - 51.5388 k1 - 0.0000243176 k2 +
0.152106 b ^ 2, -74564.1 - 1.17601 * 10 ^ -9 k1 - 0.169922 k2 -
0.0160892 b ^ 2, -139509. - 2.40194 * 10 ^ -9 k1 - 0.157372 k2 -
0.0454974 b ^ 2, -13622.5 - 2.35618 * 10 ^ -10 k1 - 0.0000178775 k2 -
0.006816 b ^ 2, -13564.5 - 9.18755 * 10 ^ -13 k1 - 5.04443 * 10 ^ -7 k2 +
0.00780019 b ^ 2,
718940. + 500,551 k1 + 0.428303 k2 - 1.41795 b ^ 2, -21055.3 -
23.3043 k1 - 1.45362 * 10 ^ -6 k2 + 0.0666351 b ^ 2, -145331. -
2.66865 * 10 ^ -9 k1 - 0.122789 k2 - 0.0507012 b ^ 2,
613,183 - 1,01045 * 10 ^ -10 k1 + 0.0000373002 k2 -
0.00251461 b ^ 2}, {126793. - 9.34595 * 10 ^ -9 k1 + 2780.26 k2 -
15.6955 b ^ 2, -522099. - 1.31878 * 10 ^ -8 k1 + 2261.69 k2 -
6.9699 b ^ 2,
1.31625 * 10 ^ 6 + 1.32172 * 10 ^ -8 k1 + 1.57742 * 10 ^ -9 k2 -
10.1835 b ^ 2, -74564.1 - 1.17601 * 10 ^ -9 k1 - 0.169922 k2 -
0.0160892 b ^ 2, -413088. - 2.6834 * 10 ^ -20 k1 - 1187.35 k2 +
8.94374 b ^ 2, -155164. - 5.48072 * 10 ^ -20 k1 - 1099.65 k2 +
3.36173 b ^ 2,
45802.1 - 5.37631 * 10 ^ -21 k1 - 0.124921 k2 -
0.992499 b ^ 2, -31.3605 - 2.09641 * 10 ^ -23 k1 - 0.00352486 k2 +
0.0000116161 b ^ 2,
1.15636 * 10 ^ 6 + 1.14215 * 10 ^ -8 k1 + 2992.82 k2 -
9.20781 b ^ 2, -14130.2 - 5.31756 * 10 ^ -10 k1 - 0.0101574 k2 -
0.431012 b ^ 2,
2.37586 - 6.08931 * 10 ^ -20 k1 - 858.001 k2 -
8.16204 * 10 ^ -7 b ^ 2, -108.193 - 2.30564 * 10 ^ -21 k1 + 0.260639 k2 -
0.00288933 b ^ 2}, {64244.2 - 1.90887 * 10 ^ -8 k1 + 2574.91 k2 -
7.95115 b ^ 2,
295696. - 2.69355 * 10 ^ -8 k1 + 2094.64 k2 - 6.40372 b ^ 2, -31.4777 +
2.69954 * 10 ^ -8 k1 + 1.46091 * 10 ^ -9 k2 +
0.000244454 b ^ 2, -139509. - 2.40194 * 10 ^ -9 k1 - 0.157372 k2 -
0.0454974 b ^ 2, -155164. - 5.48072 * 10 ^ -20 k1 - 1099.65 k2 +
3.36173 b ^ 2, -926805. - 1.11941 * 10 ^ -19 k1 - 1018.43 k2 +
2.94103 b ^ 2, -148344. - 1.09809 * 10 ^ -20 k1 - 0.115695 k2 -
0.0490629 b ^ 2,
8524.49 - 4.28181 * 10 ^ -23 k1 - 0.00326451 k2 - 0.00548197 b ^ 2,
3.95654 * 10 ^ 6 + 2.33279 * 10 ^ -8 k1 + 2771.77 k2 -
7.81479 b ^ 2, -126243. - 1.08609 * 10 ^ -9 k1 - 0.00940712 k2 -
0.0403184 b ^ 2, -1.134 * 10 ^ 6 - 1.24371 * 10 ^ -19 k1 - 794.628 k2 +
2.24037 b ^ 2,
5341.79 - 4.70916 * 10 ^ -21 k1 + 0.241388 k2 -
0.016643 b ^ 2}, {-10781.2 - 1.8725 * 10 ^ -9 k1 + 0.292511 k2 +
1.33767 b ^ 2,
151362. - 2.64224 * 10 ^ -9 k1 + 0.237952 k2 +
0.0314201 b ^ 2, -243037. + 2.64812 * 10 ^ -9 k1 + 1.6596 * 10 ^ -13 k2 +
1.88102 b ^ 2, -13622.5 - 2.35618 * 10 ^ -10 k1 - 0.0000178775 k2 -
0.006816 b ^ 2,
45802.1 - 5.37631 * 10 ^ -21 k1 - 0.124921 k2 -
0.992499 b ^ 2, -148344. - 1.09809 * 10 ^ -20 k1 - 0.115695 k2 -
0.0490629 b ^ 2, -37896.2 - 1.07717 * 10 ^ -21 k1 - 0.000013143 k2 +
0.172808 b ^ 2, -248.398 - 4.20024 * 10 ^ -24 k1 - 3.70851 * 10 ^ -7 k2 +
0.00116987 b ^ 2,
537479. + 2.28835 * 10 ^ -9 k1 + 0.314875 k2 +
0.192445 b ^ 2, -22369.3 - 1.0654 * 10 ^ -10 k1 - 1.06866 * 10 ^ -6 k2 +
0.0709145 b ^ 2, -219083. - 1.22002 * 10 ^ -20 k1 - 0.0902704 k2 +
0.432727 b ^ 2,
651.855 - 4.61945 * 10 ^ -22 k1 + 0.0000274219 k2 -
0.00258701 b ^ 2}, {-2.07898 - 7.30152 * 10 ^ -12 k1 + 0.00825368 k2 +
0.0000109055 b ^ 2, -5.60481 - 1.0303 * 10 ^ -11 k1 + 0.0067142 k2 +
0.0000107143 b ^ 2,
13.4875 + 1.03259 * 10 ^ -11 k1 + 4.68284 * 10 ^ -15 k2 -
0.0000171871 b ^ 2, -13564.5 - 9.18755 * 10 ^ -13 k1 -
5.04443 * 10 ^ -7 k2 + 0.00780019 b ^ 2, -31.3605 -
2.09641 * 10 ^ -23 k1 - 0.00352486 k2 + 0.0000116161 b ^ 2,
8524.49 - 4.28181 * 10 ^ -23 k1 - 0.00326451 k2 -
0.00548197 b ^ 2, -248.398 - 4.20024 * 10 ^ -24 k1 -
3.70851 * 10 ^ -7 k2 + 0.00116987 b ^ 2, -8.11709 * 10 ^ 7 -
1.63782 * 10 ^ -26 k1 - 1.04641 * 10 ^ -8 k2 + 39.25 b ^ 2,
9474.45 + 8.92308 * 10 ^ -12 k1 + 0.0088847 k2 -
0.00562637 b ^ 2, -44.0457 - 4.15435 * 10 ^ -13 k1 -
3.01538 * 10 ^ -8 k2 + 0.000136984 b ^ 2, -58.9499 -
4.75727 * 10 ^ -23 k1 - 0.00254712 k2 + 0.0000461921 b ^ 2,
12987.1 - 1.80128 * 10 ^ -24 k1 + 7.73752 * 10 ^ -7 k2 -
0.00461317 b ^ 2}, {-76688.6 + 3977.98 k1 - 7007.88 k2 +
9.49819 b ^ 2,
107.591 + 5613.22 k1 - 5700.77 k2 -
0.00126411 b ^ 2, -2.29463 * 10 ^ 6 - 5625.71 k1 - 3.97602 * 10 ^ -9 k2 +
17.7514 b ^ 2, 718940. + 500.551 k1 + 0.428303 k2 - 1.41795 b ^ 2,
1.15636 * 10 ^ 6 + 1.14215 * 10 ^ -8 k1 + 2992.82 k2 - 9.20781 b ^ 2
3.95654 * 10 ^ 6 + 2.33279 * 10 ^ -8 k1 + 2771.77 k2 - 7.81479 b ^ 2,
537479. + 2.28835 * 10 ^ -9 k1 + 0.314875 k2 + 0.192445 b ^ 2,
9474.45 + 8.92308 * 10 ^ -12 k1 + 0.0088847 k2 -
0.00562637 b ^ 2, -1.84704 * 10 ^ 7 - 4861.42 k1 - 7543.66 k2 +
36.4663 b ^ 2, 558416. + 226.335 k1 + 0.0256025 k2 - 0.570828 b ^ 2,
4.6185 * 10 ^ 6 + 2.59183 * 10 ^ -8 k1 + 2162.66 k2 -
5.84389 b ^ 2, -38916.3 + 9.81364 * 10 ^ -10 k1 - 0.656963 k2 +
0.0762635 b ^ 2}, {-9234.46 - 185.204 k1 + 0.0237841 k2 +
1.14341 b ^ 2, 26886.8 - 261.336 k1 + 0.0193479 k2 + 0.821086 b ^ 2,
29.4428 + 261.918 k1 + 1.34942 * 10 ^ -14 k2 -
0.00009334 b ^ 2, -21055.3 - 23.3043 k1 - 1.45362 * 10 ^ -6 k2 +
0.0666351 b ^ 2, -14130.2 - 5.31756 * 10 ^ -10 k1 - 0.0101574 k2 -
0.431012 b ^ 2, -126243. - 1.08609 * 10 ^ -9 k1 - 0.00940712 k2 -
0.0403184 b ^ 2, -22369.3 - 1.0654 * 10 ^ -10 k1 - 1.06866 * 10 ^ -6 k2 +
0.0709145 b ^ 2, -44.0457 - 4.15435 * 10 ^ -13 k1 - 3.01538 * 10 ^ -8 k2 +
0.000136984 b ^ 2,
558416. + 226.335 k1 + 0.0256025 k2 - 0.570828 b ^ 2, -19197.2 -
10.5375 k1 - 8.68923 * 10 ^ -8 k2 + 0.0608603 b ^ 2, -160055. -
1.20669 * 10 ^ -9 k1 - 0.00733987 k2 + 0.163588 b ^ 2,
767.742 - 4.56897 * 10 ^ -11 k1 + 2.22967 * 10 ^ -6 k2 -
0.00230975 b ^ 2}, {22001. - 2.12083 * 10 ^ -8 k1 + 2009.06 k2 -
2.72346 b ^ 2,
631401. - 2.99265 * 10 ^ -8 k1 + 1634.33 k2 - 5.02847 b ^ 2, -657764. +
2.99931 * 10 ^ -8 k1 + 1.13987 * 10 ^ -9 k2 + 5.08896 b ^ 2, -145331. -
2.66865 * 10 ^ -9 k1 - 0.122789 k2 - 0.0507012 b ^ 2,
2.37586 - 6.08931 * 10 ^ -20 k1 - 858.001 k2 -
8.16204 * 10 ^ -7 b ^ 2, -1.134 * 10 ^ 6 - 1.24371 * 10 ^ -19 k1 -
794,628 k2 + 2.24037 b ^ 2, -219083. - 1.22002 * 10 ^ -20 k1 -
0.0902704 k2 + 0.432727 b ^ 2, -58.9499 - 4.75727 * 10 ^ -23 k1 -
0.00254712 k2 + 0.0000461921 b ^ 2,
4.6185 * 10 ^ 6 + 2.59183 * 10 ^ -8 k1 + 2162.66 k2 -
5.84389 b ^ 2, -160055. - 1.20669 * 10 ^ -9 k1 - 0.00733987 k2 +
0.163588 b ^ 2, -1.51759 * 10 ^ 6 - 1.38182 * 10 ^ -19 k1 - 620.006 k2 +
2.99673 b ^ 2,
11219.2 - 5.23207 * 10 ^ -21 k1 + 0.188342 k2 -
0.0216322 b ^ 2}, {65.6162 - 8.03025 * 10 ^ -10 k1 - 0.610304 k2 +
0.00145184 b ^ 2, -638.944 - 1.13313 * 10 ^ -9 k1 - 0.49647 k2 +
0.00477873 b ^ 2,
754.94 + 1.13565 * 10 ^ -9 k1 - 3.46264 * 10 ^ -13 k2 + 0.000759213 b ^ 2,
613,183 - 1,01045 * 10 ^ -10 k1 + 0.0000373002 k2 -
0.00251461 b ^ 2, -108.193 - 2.30564 * 10 ^ -21 k1 + 0.260639 k2 -
0.00288933 b ^ 2,
5341.79 - 4.70916 * 10 ^ -21 k1 + 0.241388 k2 - 0.016643 b ^ 2,
651.855 - 4.61945 * 10 ^ -22 k1 + 0.0000274219 k2 - 0.00258701 b ^ 2,
12987.1 - 1.80128 * 10 ^ -24 k1 + 7.73752 * 10 ^ -7 k2 -
0.00461317 b ^ 2, -38916.3 + 9.81364 * 10 ^ -10 k1 - 0.656963 k2 +
0.0762635 b ^ 2,
767.742 - 4.56897 * 10 ^ -11 k1 + 2.22967 * 10 ^ -6 k2 - 0.00230975 b ^ 2
11219.2 - 5.23207 * 10 ^ -21 k1 + 0.188342 k2 -
0.0216322 b ^ 2, -1249.8 - 1.98106 * 10 ^ -22 k1 - 0.0000572138 k2 +
0.000444287 b ^ 2}};
MatrixForm[R]
P = simplify[Det[Det[Det[Det[R]]NSolve[{P == 0, 0 < b < 100000000}, b]
``````

I have a 12 cross system 12, I have taken the determinant, the determining function depends on a single variable `second`. Now I'm trying to find the roots of that. `det` function. `NSolve` It is taking too long. What is the best way to find the roots.