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Solution - Polynomial root calculator

x = - 0.885593

x=-0.885593

x = 0.692786

x=0.692786

x = 4.329114

x=4.329114

x = - 0.068 - 1.734 i

x=-0.068-1.734i

x = - 0.068 + 1.734 i

x=-0.068+1.734i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{5} - 4 x^{4} + x^{3} - 10 x^{2} - 4 x + 8 = 0$

$a_{n} = 1$

$a_{0} = 8$

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, -2, 2, -4, 4, -8, 8. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 4, 8$

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

$x = + / - p / q = - 1, 1, - 2, 2, - 4, 4, - 8, 8$

$P (- 1) = - 4$

$P (1) = - 8$

$P (- 2) = - 128$

$P (2) = - 64$

$P (- 4) = - 2248$

$P (4) = - 104$

$P (- 8) = - 50264$

$P (8) = 16232$

3. Solve the remaining factor

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

$x = 4.329114, - 0.068153 + 1.734178 i, 0.692786, - 0.885593, - 0.068153 - 1.734178 i$

4. Collect all roots

All roots with multiplicity: x={-0.885593,0.692786,4.329114,-0.068153-1.734178i,-0.068153+1.734178i}.

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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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