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Solution - Polynomial root calculator

x = 2.837722

x=2.837722

x = 6

x=6

x = 6

x=6

x = 9.162278

x=9.162278

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{4} - 24 x^{3} + 206 x^{2} - 744 x + 936 = 0$

$a_{n} = 1$

$a_{0} = 936$

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, -3, 3, -4, 4, -6, 6, -8, 8, -9, 9, -12, 12, -13, 13, -18, 18, -24, 24, -26, 26, -36, 36, -39, 39, -52, 52, -72, 72, -78, 78, -104, 104, -117, 117, -156, 156, -234, 234, -312, 312, -468, 468, -936, 936. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 3, 4, 6, 8, 9, 12, 13, 18, 24, 26, 36, 39, 52, 72, 78, 104, 117, 156, 234, 312, 468, 936$

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

$x = + / - p / q = - 1, 1, - 2, 2, - 3, 3, - 4, 4, - 6, 6, - 8, 8, - 9, 9, - 12, 12, - 13, 13, - 18, 18, - 24, 24, - 26, 26, - 36, 36, - 39, 39, - 52, 52, - 72, 72, - 78, 78, - 104, 104, - 117, 117, - 156, 156, - 234, 234, - 312, 312, - 468, 468, - 936, 936$

$P (- 1) = 1911$

$P (1) = 375$

$P (- 2) = 3456$

$P (2) = 96$

$P (- 3) = 5751$

$P (3) = - 9$

$P (- 4) = 9000$

$P (4) = - 24$

$P (- 6) = 19296$

$P (6) = 0$

$(x - 6) (x^{3} - 18 x^{2} + 98 x - 156) = 0$

$(x - 6) (x^{2} - 12 x + 26) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = 2.837722, 9.162278$

4. Collect all roots

All roots with multiplicity: x={2.837722,6,6,9.162278}.

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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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