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Soluție - PolynomialRootFinder

x=2,837722
x=2,837722
x=6
x=6
x=6
x=6
x=9,162278
x=9,162278

Alte moduri de a rezolva

PolynomialRootFinder

Explicații pas cu pas

1. Normalizeaza la P(x)=0

x424x3+206x2744x+936=0

an=1

a0=936

Rescrie ecuatia ca polinom egal cu zero.

2. Testeaza radacinile candidate

Posibile radacini rationale: -1, 1, -2, 2, -3, 3, -4, 4, -6, 6, -8, 8, -9, 9, -12, 12, -13, 13, -18, 18, -24, 24, -26, 26, -36, 36, -39, 39, -52, 52, -72, 72, -78, 78, -104, 104, -117, 117, -156, 156, -234, 234, -312, 312, -468, 468, -936, 936. Testeaza fiecare candidat si deflateaza factorii descoperiti.

factors(|a0|)=1,2,3,4,6,8,9,12,13,18,24,26,36,39,52,72,78,104,117,156,234,312,468,936

factors(|an|)=1

x=+/-p/q=-1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-9,9,-12,12,-13,13,-18,18,-24,24,-26,26,-36,36,-39,39,-52,52,-72,72,-78,78,-104,104,-117,117,-156,156,-234,234,-312,312,-468,468,-936,936

P(1)=1911

P(1)=375

P(2)=3456

P(2)=96

P(3)=5751

P(3)=9

P(4)=9000

P(4)=24

P(6)=19296

P(6)=0

(x6)(x318x2+98x156)=0

(x6)(x212x+26)=0

3. Rezolva factorul ramas

Rezolva polinomul ramas folosind formula patratica.

x=2,837722,9,162278

4. Colecteaza toate radacinile

Toate radacinile cu multiplicitate: x={2.837722,6,6,9.162278}.

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