Enter an equation or problem

Camera input is not recognized!

Solution - Polynomial root calculator

x = - 6

x=-6

x = - 4

x=-4

x = 8

x=8

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$x^{3} + 2 x^{2} - 56 x - 192 = 0$

$a_{n} = 1$

$a_{0} = - 192$

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, -12, 12, -16, 16, -24, 24, -32, 32, -48, 48, -64, 64, -96, 96, -192, 192. Evaluate P(c) for each candidate and deflate when P(c)=0.

$f a c t o r s (| a_{0} |) = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192$

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

$x = + / - p / q = - 1, 1, - 2, 2, - 3, 3, - 4, 4, - 6, 6, - 8, 8, - 12, 12, - 16, 16, - 24, 24, - 32, 32, - 48, 48, - 64, 64, - 96, 96, - 192, 192$

$P (- 1) = - 135$

$P (1) = - 245$

$P (- 2) = - 80$

$P (2) = - 288$

$P (- 3) = - 33$

$P (3) = - 315$

$P (- 4) = 0$

$(x + 4) (x^{2} - 2 x - 48) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 6, 8$

4. Collect all roots

All roots with multiplicity: x={-6,-4,8}.

Was this explanation helpful?

Yes No

How did we do?

Please leave us feedback.

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

Latest Related Drills Solved