SOLUTION: State the degree of each polynomial equation. Find all of the real and imaginary roots of each equation, stating multiplicity when it is greater than one. x^3 - 4x^2 - 6x = 0

Algebra.Com
Question 728317: State the degree of each polynomial equation. Find all of the real and imaginary roots of each equation, stating multiplicity when it is greater than one.
x^3 - 4x^2 - 6x = 0
I know that the degree is 3 because of the highest power shown. but i was thinking that i should use the quadratic equation to find the multiplicity. i was wrong according to the answer section...2 +/- sqrt 10 please, can you show the work so that i can understand this problem
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
x³ - 4x² - 6x = 0

Factor x out of the left side:

x(x² - 4x - 6) = 0

We use the zero factor property:

x = 0;   x² - 4x - 6 = 0

         x = 
         x = 
         x =          
         x = 
         x = 
         x = 
         x = 
         x = 
         x = 2±√10

So there are three solutions:

0, 2+√10, 2-√10

All have multiplicity 1, because there are the same number of
different solutions as the degree, which is 3.
 
Edwin
RELATED QUESTIONS

State the degree of the following polynomial equation. Find all of the real and imaginary (answered by ewatrrr)
Find all of the real and imaginary roots, stating the multiplicity of each. 16) (x +... (answered by edjones)
Find all of the real and imaginary roots, stating the multiplicity of each. 16) (x +... (answered by stanbon)
Find all real and imaginary zeros of the following polynomial equation: m(x)=... (answered by stanbon)
Use the Rational Root Theorem to find all the roots of each equation. 4. x'3 +... (answered by stanbon)
Find all real and imaginary roots of this equation:... (answered by lwsshak3)
Which describes the number and type of roots of the equation x^2 + 121x = 0 a) 1 real... (answered by richwmiller)
Which describes the number and type of roots of the equation x^2 + 121x = 0 a) 1 real... (answered by richwmiller)
Find all of the rational roots of each polynomial equation 2xsquared + 3x + 1 =... (answered by stanbon)