Polynomial roots calculator

This free math tool finds the roots (zeros) of a given polynomial. The calculator computes exact solutions for quadratic, cubic, and quartic equations. Calculator shows all the work and provides step-by-step on how to find zeros and their multiplicities.

ID	Problem	Count
1	Find roots of polynomial $$ p(x) = -120x^7-420x^6+2790x^5+10050x^4-15600x^3-64440x^2+960x+74880 $$	121
2	Find roots of polynomial $$ p(x) = x^2-4x+3 $$	114
3	Find roots of polynomial $$ p(x) = 2x^2+3x-14 $$	85
4	Find roots of polynomial $$ p(x) = 2x^3-4x^2-3x+6 $$	72
5	Find roots of polynomial $$ p(x) = x^6+x^5+x^4+x^3+7x^2+5x+2 $$	71
6	Find roots of polynomial $$ p(x) = 4x^2-10x+4 $$	70
7	Find roots of polynomial $$ p(x) = x^3-6x^2+11x-6 $$	70
8	Find roots of polynomial $$ p(x) = 12x^4+17x^3-22x^2-13x+6 $$	63
9	Find roots of polynomial $$ p(x) = x^3-2x^2-5x+6 $$	56
10	Find roots of polynomial $$ p(x) = x^3-3x^2-11x+21 $$	55
11	Find roots of polynomial $$ p(x) = 2x^5-x^4-14x^3-6x^2+24x+40 $$	54
12	Find roots of polynomial $$ p(x) = 4x^3+12x^2+12x+10 $$	54
13	Find roots of polynomial $$ p(x) = x $$	53
14	Find roots of polynomial $$ p(x) = x^3-x^2-44x-96 $$	51
15	Find roots of polynomial $$ p(x) = x^4-13x $$	51
16	Find roots of polynomial $$ p(x) = 2x^2+3x $$	51
17	Find roots of polynomial $$ p(x) = x^4-5x^2+4 $$	50
18	Find roots of polynomial $$ p(x) = x^3+9x^2+6x-16 $$	50
19	Find roots of polynomial $$ p(x) = x^3-2x^2-x+2 $$	49
20	Find roots of polynomial $$ p(x) = 6x^3-25x^2+2x+8 $$	47
21	Find roots of polynomial $$ p(x) = 10x^8-290x^7+3600x^6-24900x^5+104490x^4-270810x^3+419900x^2-352000x+120000 $$	46
22	Find roots of polynomial $$ p(x) = x^4+4x^3+6x^2+4x+1 $$	45
23	Find roots of polynomial $$ p(x) = 42x^6-12x^5+20x^4+8x^3-3000000x^2+18x+1 $$	45
24	Find roots of polynomial $$ p(x) = 2x^5+4x^3 $$	41
25	Find roots of polynomial $$ p(x) = 14x^6+54x^5-375x^4-1268x^3+2115x^2+5400x $$	41
26	Find roots of polynomial $$ p(x) = x^2+1 $$	41
27	Find roots of polynomial $$ p(x) = 2x^7+9x^6-75x^5-317x^4+705x^3+2700x^2 $$	41
28	Find roots of polynomial $$ p(x) = x^3-3x^2+3x-1 $$	40
29	Find roots of polynomial $$ p(x) = x^3-1 $$	40
30	Find roots of polynomial $$ p(x) = 80x^7-2030x^6+21600x^5-124500x^4+417960x^3-812430x^2+839800x-352000 $$	40
31	Find roots of polynomial $$ p(x) = -x^5+4x^4+x^3-15x^2+12x+4 $$	39
32	Find roots of polynomial $$ p(x) = x^4+9x^3-44x^2-236x+1440 $$	39
33	Find roots of polynomial $$ p(x) = x^4+2x^3-47x^2-48x+252 $$	38
34	Find roots of polynomial $$ p(x) = 4x^3-21x^2+29x-6 $$	38
35	Find roots of polynomial $$ p(x) = x^2-5x+6 $$	38
36	Find roots of polynomial $$ p(x) = x^3-3x^2-10x+24 $$	38
37	Find roots of polynomial $$ p(x) = x^3+2x^2-5x-6 $$	36
38	Find roots of polynomial $$ p(x) = 2023 $$	36
39	Find roots of polynomial $$ p(x) = 8x^7+77x^6-108x^5-2360x^4-1280x^3+19728x^2+15552x-27648 $$	35
40	Find roots of polynomial $$ p(x) = x^2-2x+1 $$	35
41	Find roots of polynomial $$ p(x) = x^8-18x^6-320x^4+11x^7-472x^5+6576x^3-27648x+7776x^2-41472 $$	34
42	Find roots of polynomial $$ p(x) = x^3+3x^2+3x+1 $$	34
43	Find roots of polynomial $$ p(x) = x^3-x^2-x+1 $$	34
44	Find roots of polynomial $$ p(x) = x^2+2x+2 $$	33
45	Find roots of polynomial $$ p(x) = -x^3 $$	33
46	Find roots of polynomial $$ p(x) = 12x+26 $$	33
47	Find roots of polynomial $$ p(x) = x^2+x+1 $$	33
48	Find roots of polynomial $$ p(x) = x^3+5x^2+5x+1 $$	33
49	Find roots of polynomial $$ p(x) = x^3-48x^2+684x-2592 $$	33
50	Find roots of polynomial $$ p(x) = x^4+16x^3+47x^2-100x-132 $$	33

Polynomial roots calculator

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Polynomial Roots – Solved Problems Database