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Solution - Polynomial root calculator

x = - 1

x=-1

x = - 0.500 - 0.866 i

x=-0.500-0.866i

x = - 0.500 + 0.866 i

x=-0.500+0.866i

x = 0.500 - 0.866 i

x=0.500-0.866i

x = 0.500 + 0.866 i

x=0.500+0.866i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{5} + x^{4} + x^{3} + x^{2} + x + 1 = 0$

$a_{n} = 1$

$a_{0} = 1$

Rewrite in standard form P(x)=0, then identify the leading and constant coefficients.

2. Test candidate roots

Build rational candidates from factor ratios p/q: -1, 1. Evaluate P(c) for each candidate and deflate when P(c)=0.

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

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

$x = + / - p / q = - 1, 1$

$P (- 1) = 0$

$P (- 1) = 3$

$P (1) = 3$

$(x + 1) (x^{4} + x^{2} + 1) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using numeric approximation (Durand-Kerner).

$x = 0.5 - 0.866025 i, 0.5 + 0.866025 i, - 0.5 + 0.866025 i, - 0.5 - 0.866025 i$

4. Collect all roots

All roots with multiplicity: x={-1,-0.5-0.866025i,-0.5+0.866025i,0.5-0.866025i,0.5+0.866025i}.

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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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