Decide if the statements below are true or false. Given: f (z) = z³ – 22- 17z + 65 To find all of the roots, the first thing I should do is use the quadratic formula: Now I can see that one of the real roots is x = -5: Slnce I have a root, I should use synthetic division. (Please complete on your own). -17 +65

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Decide if the statements below are true or false.
Given: f (1) = z3 - 22 - 17x + 65
To find all of the roots, the first thing I should do is use the quadratic formula:
Now I can see that one of the real roots is x = -5:
Slnce I have a root, I should use synthetic division. (Please complete on your own).
-17
+65
In the orange box, is -5:
and in the red box, is -13:
Since there is no remainder, this means this IS a root like
we thought!
So now I have: f (r) = (x+5) (x2 - 6x + 13)::
and I need to use synthetic division again:i
Finally, my correct roots are: x = -5:i
i and x = 3+ 4i:
cer
Transcribed Image Text:Decide if the statements below are true or false. Given: f (1) = z3 - 22 - 17x + 65 To find all of the roots, the first thing I should do is use the quadratic formula: Now I can see that one of the real roots is x = -5: Slnce I have a root, I should use synthetic division. (Please complete on your own). -17 +65 In the orange box, is -5: and in the red box, is -13: Since there is no remainder, this means this IS a root like we thought! So now I have: f (r) = (x+5) (x2 - 6x + 13):: and I need to use synthetic division again:i Finally, my correct roots are: x = -5:i i and x = 3+ 4i: cer
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