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Solution - Polynomial root calculator

x = - 10

x=-10

x = - 10

x=-10

x = 5

x=5

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$- x^{3} - 15 x^{2} + 500 = 0$

$a_{n} = - 1$

$a_{0} = 500$

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, -5, 5, -10, 10, -20, 20, -25, 25, -50, 50, -100, 100, -125, 125, -250, 250, -500, 500. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500$

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

$x = + / - p / q = - 1, 1, - 2, 2, - 4, 4, - 5, 5, - 10, 10, - 20, 20, - 25, 25, - 50, 50, - 100, 100, - 125, 125, - 250, 250, - 500, 500$

$P (- 1) = 486$

$P (1) = 484$

$P (- 2) = 448$

$P (2) = 432$

$P (- 4) = 324$

$P (4) = 196$

$P (- 5) = 250$

$P (5) = 0$

$(x - 5) (- x^{2} - 20 x - 100) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 10, - 10$

4. Collect all roots

All roots with multiplicity: x={-10,-10,5}.

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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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