Polynomials

[SC611]

How can I find all the roots of a polynomial in a hp prime? For example, 3x^5+5x^4+2x^3+8x^2+3x-10=0

Thank you beforehand!

[mdklassen · Accepted solution]

Here is some "pseudo-code" to help with your high-school homework:

do x = -10 to +10

  y = x* ( x* ( x* ( x* (x*3 +5) +2)+8)+3) -10

  say x y
end

that gives the output:

-10 -251240
-9 -145189
-8 -78370
-7 -38741
-6 -17020
-5 -6325
-4 -1814
-3 -325
-2 -16
-1 -5
  0 -10
  1 11
  2 220
  3 1259
  4 4610
  5 12955
  6 30536
  7 63515
  8 120334
  9 212075
10 352820

Second try:

do xx = -20 to +20
x = xx / 10

y = x* ( x* ( x* ( x* (3*x +5) +2)+8)+3) -10

say x y
end

gives the output:

-2 -16
-1.9 -9.66047
-1.8 -5.34304
-1.7 -2.64121
-1.6 -1.20128
-1.5 -0.71875
-1.4 -0.93472
-1.3 -1.63229
-1.2 -2.63296
-1.1 -3.79303
-1 -5
-0.9 -6.16897
-0.8 -7.23904
-0.7 -8.16971
-0.6 -8.93728
-0.5 -9.53125
-0.4 -9.95072
-0.3 -10.20079
-0.2 -10.28896
-0.1 -10.22153
0 -10
0.1 -9.61747
0.2 -9.05504
0.3 -8.27821
0.4 -7.23328
0.5 -5.84375
0.6 -4.00672
0.7 -1.58929
0.8 1.57504
0.9 5.68997
1.0 11
1.1 17.79403
1.2 26.40896
1.3 37.23329
1.4 50.71072
1.5 67.34375
1.6 87.69728
1.7 112.40221
1.8 142.15904
1.9 177.74147
2 220

Looking closely:

-1.6 -1.20128
-1.5 -0.71875
-1.4 -0.93472
-1.3 -1.63229

there might possibly be a root in the [-1.6,-1.3] range.

Closer examination disproves this conjecture.

And:

0.7 -1.58929
0.8   1.57504

showing at least one root in the [0.7,0.8] range.

Stepping by 1/100 in the same range gives:

0.71 -1.3095252
0.72 -1.0221359
0.73 -0.7269325
0.74 -0.4237212
0.75 -0.1123047
0.76  0.2075184
0.77  0.5359533
0.78  0.8732091
0.79  1.2194989

showing at least one root in the [0.75,0.76] range.

I hope this helps.