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Solution - Polynomial root calculator

x = - 1.846084

x=-1.846084

x = 1.625061

x=1.625061

x = - 0.813 - 1.407 i

x=-0.813-1.407i

x = - 0.813 + 1.407 i

x=-0.813+1.407i

x = 0.923 - 1.599 i

x=0.923-1.599i

x = 0.923 + 1.599 i

x=0.923+1.599i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{6} + 2 x^{3} - 27 = 0$

$a_{n} = 1$

$a_{0} = - 27$

Rewrite the equation as a polynomial equal to zero.

2. Test candidate roots

Possible rational roots: -1, 1, -3, 3, -9, 9, -27, 27. Test each candidate and deflate when a root is found.

$f a c t o r s (| a_{0} |) = 1, 3, 9, 27$

$f a c t o r s (| a_{n} |) = 1$

$x = + / - p / q = - 1, 1, - 3, 3, - 9, 9, - 27, 27$

$P (- 1) = - 28$

$P (1) = - 24$

$P (- 3) = 648$

$P (3) = 756$

$P (- 9) = 529956$

$P (9) = 532872$

$P (- 27) = 387381096$

$P (27) = 387459828$

3. Solve the remaining factor

Solve the remaining polynomial using numeric approximation (Durand-Kerner).

$x = 1.625061, 0.923042 + 1.598756 i, - 1.846084, - 0.812531 - 1.407345 i, - 0.812531 + 1.407345 i, 0.923042 - 1.598756 i$

4. Collect all roots

All roots with multiplicity: x={-1.846084,1.625061,-0.812531-1.407345i,-0.812531+1.407345i,0.923042-1.598756i,0.923042+1.598756i}.

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Terms and topics

Polynomial root calculator

Solution - Polynomial root calculator

Step-by-step explanation

1. Normalize to P(x)=0

2. Test candidate roots

3. Solve the remaining factor

4. Collect all roots

Why learn this

Terms and topics

Related links

Solution - Polynomial root calculator

Step-by-step explanation

1. Normalize to P(x)=0

2. Test candidate roots

3. Solve the remaining factor

4. Collect all roots

Why learn this

Terms and topics

Related links

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