SOLUTION: factor the following polynomial completely into linear factors using real or complex roots. Express how many roots there are. Also, describe the graph of the function.
x^5-11x^
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Question 980149: factor the following polynomial completely into linear factors using real or complex roots. Express how many roots there are. Also, describe the graph of the function.
x^5-11x^4+13x^3-143x^2=36x-396
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^5-11x^4+13x^3-143x^2= 36x-396
x^4(x-11) + 13x^2(x-11) =36 (x-11)
(x^4+13x^2-36) (x-11)=0
x=11, 1 root
(1/2)(-13 +/- sqrt (169+144)) ;; sqrt 313=17.69
(1/2) (-13+/-17.69)
x^2=-30.69
x=+/- i sqrt(30.69)
x^2=2.345
x=+/- 1.531
There are 3 real roots, 11 and a conjugate pair of irrational roots.
There are two complex roots.
The graph goes from minus infinity through the negative irrational root, peaks at y=396 at x=0, and then descends through the positive rational root and then ascends again, crossing the x-axis at x=11 ascending to infinity.
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