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Solution - Polynomial root calculator

x = 2.5

x=2.5

x = - 0.500 - 0.866 i

x=-0.500-0.866i

x = - 0.500 + 0.866 i

x=-0.500+0.866i

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$2 x^{3} - 3 x^{2} - 3 x - 5 = 0$

$a_{n} = 2$

$a_{0} = - 5$

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

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

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

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

$P (- 1 / 2) = - 4.5$

$P (1 / 2) = - 7$

$P (- 1) = - 7$

$P (1) = - 9$

$P (- 5 / 2) = - 47.5$

$P (5 / 2) = 0$

$(x - 2.5) (2 x^{2} + 2 x + 2) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 0.5 - 0.866025 i, - 0.5 + 0.866025 i$

4. Collect all roots

All roots with multiplicity: x={2.5,-0.5-0.866025i,-0.5+0.866025i}.

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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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