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Solution - Polynomial root calculator

x = 0.303365

x=0.303365

x = 5.44313

x=5.44313

x = - 1.010 - 0.837 i

x=-1.010-0.837i

x = - 1.010 + 0.837 i

x=-1.010+0.837i

x = 0.386 - 0.450 i

x=0.386-0.450i

x = 0.386 + 0.450 i

x=0.386+0.450i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$2 x^{6} - 9 x^{5} - 10 x^{4} - 3 x^{3} + 10 x^{2} - 9 x + 2 = 0$

$a_{n} = 2$

$a_{0} = 2$

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

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

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

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

$P (- 1 / 2) = 9.0625$

$P (1 / 2) = - 1.25$

$P (- 1) = 25$

$P (1) = - 17$

$P (- 2) = 340$

$P (2) = - 320$

3. Solve the remaining factor

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

$x = 5.44313, 0.386329 + 0.450453 i, - 1.009577 + 0.836921 i, 0.303365, - 1.009577 - 0.836921 i, 0.386329 - 0.450453 i$

4. Collect all roots

All roots with multiplicity: x={0.303365,5.44313,-1.009577-0.836921i,-1.009577+0.836921i,0.386329-0.450453i,0.386329+0.450453i}.

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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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