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Solution - Polynomial root calculator

x = - 0.333333

x=-0.333333

x = 0

x=0

x = 0.333333

x=0.333333

x = 7

x=7

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$9 x^{4} - 63 x^{3} - x^{2} + 7 x = 0$

$a_{n} = 9$

$a_{0} = 0$

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: -1/9, 1/9, -1/3, 1/3, -7/9, 7/9, -1, 1, -7/3, 7/3, -7, 7. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 7$

$f a c t o r s (| a_{n} |) = 1, 3, 9$

$x = + / - p / q = - 1 / 9, 1 / 9, - 1 / 3, 1 / 3, - 7 / 9, 7 / 9, - 1, 1, - 7 / 3, 7 / 3, - 7, 7$

$P (- 1 / 9) = 6.320988$

$P (1 / 9) = 6.123457$

$P (- 1 / 3) = 0$

$x (9 x^{3} - 63 x^{2} - x + 7) = 0$

$(x + 0.333333) (9 x^{2} - 66 x + 21) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = 0.333333, 7$

4. Collect all roots

All roots with multiplicity: x={-0.333333,0,0.333333,7}.

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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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