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Solution - Polynomial root calculator

x = 0.50866

x=0.50866

x = - 1.012 - 0.684 i

x=-1.012-0.684i

x = - 1.012 + 0.684 i

x=-1.012+0.684i

x = 0.258 - 1.119 i

x=0.258-1.119i

x = 0.258 + 1.119 i

x=0.258+1.119i

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.

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

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

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

$P (- 1) = - 2$

$P (1) = 4$

3. Solve the remaining factor

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

$x = 0.50866, 0.257507 + 1.11879 i, - 1.011837 + 0.683959 i, - 1.011837 - 0.683959 i, 0.257507 - 1.11879 i$

4. Collect all roots

All roots with multiplicity: x={0.50866,-1.011837-0.683959i,-1.011837+0.683959i,0.257507-1.11879i,0.257507+1.11879i}.

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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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