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Solution - Polynomial root calculator

x = - 1.414214

x=-1.414214

x = 1.414214

x=1.414214

x = 0.000 - 1.291 i

x=0.000-1.291i

x = 0.000 + 1.291 i

x=0.000+1.291i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

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

$a_{n} = 3$

$a_{0} = - 10$

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: -1/3, 1/3, -2/3, 2/3, -1, 1, -5/3, 5/3, -2, 2, -10/3, 10/3, -5, 5, -10, 10. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 5, 10$

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

$x = + / - p / q = - 1 / 3, 1 / 3, - 2 / 3, 2 / 3, - 1, 1, - 5 / 3, 5 / 3, - 2, 2, - 10 / 3, 10 / 3, - 5, 5, - 10, 10$

$P (- 1 / 3) = - 10.074074$

$P (1 / 3) = - 10.074074$

$P (- 2 / 3) = - 9.851852$

$P (2 / 3) = - 9.851852$

$P (- 1) = - 8$

$P (1) = - 8$

$P (- 5 / 3) = 10.37037$

$P (5 / 3) = 10.37037$

$P (- 2) = 34$

$P (2) = 34$

3. Solve the remaining factor

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

$x = 1.414214, - 1.290994 i, 1.290994 i, - 1.414214$

4. Collect all roots

All roots with multiplicity: x={-1.414214,1.414214,-1.290994i,1.290994i}.

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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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