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Solution - Polynomial root calculator

x = - 1

x=-1

x = - 0.285714

x=-0.285714

x = 0.25

x=0.25

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$84 x^{3} + 87 x^{2} - 3 x - 6 = 0$

$a_{n} = 84$

$a_{0} = - 6$

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: -1/84, 1/84, -1/42, 1/42, -1/28, 1/28, -1/21, 1/21, -1/14, 1/14, -1/12, 1/12, -2/21, 2/21, -3/28, 3/28, -1/7, 1/7, -1/6, 1/6, -3/14, 3/14, -1/4, 1/4, -2/7, 2/7, -1/3, 1/3, -3/7, 3/7, -1/2, 1/2, -2/3, 2/3, -3/4, 3/4, -6/7, 6/7, -1, 1, -3/2, 3/2, -2, 2, -3, 3, -6, 6. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 3, 6$

$f a c t o r s (| a_{n} |) = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$

$x = + / - p / q = - 1 / 84, 1 / 84, - 1 / 42, 1 / 42, - 1 / 28, 1 / 28, - 1 / 21, 1 / 21, - 1 / 14, 1 / 14, - 1 / 12, 1 / 12, - 2 / 21, 2 / 21, - 3 / 28, 3 / 28, - 1 / 7, 1 / 7, - 1 / 6, 1 / 6, - 3 / 14, 3 / 14, - 1 / 4, 1 / 4, - 2 / 7, 2 / 7, - 1 / 3, 1 / 3, - 3 / 7, 3 / 7, - 1 / 2, 1 / 2, - 2 / 3, 2 / 3, - 3 / 4, 3 / 4, - 6 / 7, 6 / 7, - 1, 1, - 3 / 2, 3 / 2, - 2, 2, - 3, 3, - 6, 6$

$P (- 1 / 84) = - 5.952098$

$P (1 / 84) = - 6.023243$

$P (- 1 / 42) = - 5.880385$

$P (1 / 42) = - 6.020975$

$P (- 1 / 28) = - 5.785714$

$P (1 / 28) = - 5.992347$

$P (- 1 / 21) = - 5.668934$

$P (1 / 21) = - 5.936508$

$P (- 1 / 14) = - 5.372449$

$P (1 / 14) = - 5.739796$

$(x - 0.25) (84 x^{2} + 108 x + 24) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 1, - 0.285714$

4. Collect all roots

All roots with multiplicity: x={-1,-0.285714,0.25}.

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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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