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Solution - Polynomial root calculator

x = - 1

x=-1

x = 0.000 - 2.000 i

x=0.000-2.000i

x = 0.000 + 2.000 i

x=0.000+2.000i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{3} + x^{2} + 4 x + 4 = 0$

$a_{n} = 1$

$a_{0} = 4$

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. Evaluate P(c) for each candidate and deflate when P(c)=0.

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

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

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

$P (- 1) = 0$

$(x + 1) (x^{2} + 4) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 2 i, 2 i$

4. Collect all roots

All roots with multiplicity: x={-1,-2i,2i}.

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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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