Enter an equation or problem

Camera input is not recognized!

Solution - Polynomial root calculator

x = - 3

x=-3

x = - 1

x=-1

x = - 0.333333

x=-0.333333

x = 0.5

x=0.5

x = 2

x=2

See steps Try this:

Step-by-step explanation

1. Normalize to P(x)=0

$6 x^{5} + 11 x^{4} - 33 x^{3} - 33 x^{2} + 11 x + 6 = 0$

$a_{n} = 6$

$a_{0} = 6$

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: -1/6, 1/6, -1/3, 1/3, -1/2, 1/2, -2/3, 2/3, -1, 1, -3/2, 3/2, -2, 2, -3, 3, -6, 6. Evaluate P(c) for each candidate and deflate when P(c)=0.

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

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

$x = + / - p / q = - 1 / 6, 1 / 6, - 1 / 3, 1 / 3, - 1 / 2, 1 / 2, - 2 / 3, 2 / 3, - 1, 1, - 3 / 2, 3 / 2, - 2, 2, - 3, 3, - 6, 6$

$P (- 1 / 6) = 3.410494$

$P (1 / 6) = 6.773148$

$P (- 1 / 3) = 0$

$P (- 1 / 6) = 20.462963$

$P (1 / 6) = 13.546296$

$P (- 1 / 3) = 20.740741$

$P (1 / 3) = 7.407407$

$P (- 1 / 2) = 18.75$

$P (1 / 2) = 0$

$P (- 1 / 6) = - 30.694444$

$(x + 0.333333) (6 x^{4} + 9 x^{3} - 36 x^{2} - 21 x + 18) = 0$

$(x - 0.5) (6 x^{3} + 12 x^{2} - 30 x - 36) = 0$

$(x + 1) (6 x^{2} + 6 x - 36) = 0$

3. Solve the remaining factor

After deflation, solve the remaining factor using quadratic formula.

$x = - 3, 2$

4. Collect all roots

All roots with multiplicity: x={-3,-1,-0.333333,0.5,2}.

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