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Solution - Polynomial root calculator

x = - 1.628822

x=-1.628822

x = 0.399107

x=0.399107

x = 9.229716

x=9.229716

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{3} - 8 x^{2} - 12 x + 6 = 0$

$a_{n} = 1$

$a_{0} = 6$

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, -3, 3, -6, 6. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 3, 6$

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

$x = + / - p / q = - 1, 1, - 2, 2, - 3, 3, - 6, 6$

$P (- 1) = 9$

$P (1) = - 13$

$P (- 2) = - 10$

$P (2) = - 42$

$P (- 3) = - 57$

$P (3) = - 75$

$P (- 6) = - 426$

$P (6) = - 138$

3. Solve the remaining factor

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

$x = 9.229716, - 1.628822, 0.399107$

4. Collect all roots

All roots with multiplicity: x={-1.628822,0.399107,9.229716}.

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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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