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Solution - Polynomial root calculator

x = - 1.366 - 0.366 i

x=-1.366-0.366i

x = - 1.366 + 0.366 i

x=-1.366+0.366i

x = 0.366 - 1.366 i

x=0.366-1.366i

x = 0.366 + 1.366 i

x=0.366+1.366i

x = 1.000 - 1.000 i

x=1.000-1.000i

x = 1.000 + 1.000 i

x=1.000+1.000i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{6} + 4 x^{3} + 8 = 0$

$a_{n} = 1$

$a_{0} = 8$

Rewrite the equation as a polynomial equal to zero.

2. Test candidate roots

Possible rational roots: -1, 1, -2, 2, -4, 4, -8, 8. Test each candidate and deflate when a root is found.

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

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

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

$P (- 1) = 5$

$P (1) = 13$

$P (- 2) = 40$

$P (2) = 104$

$P (- 4) = 3848$

$P (4) = 4360$

$P (- 8) = 260104$

$P (8) = 264200$

3. Solve the remaining factor

Solve the remaining polynomial using numeric approximation (Durand-Kerner).

$x = 1 + i, - 1.366025 + 0.366025 i, 0.366025 + 1.366025 i, 1 - i, - 1.366025 - 0.366025 i, 0.366025 - 1.366025 i$

4. Collect all roots

All roots with multiplicity: x={-1.366025-0.366025i,-1.366025+0.366025i,0.366025-1.366025i,0.366025+1.366025i,1-i,1+i}.

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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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