Chupa T.

asked • 05/14/17

Find the roots of the equation: x^3-4x^2+2x-10=x^2-5x-3

This equation has a complex root of +3, ±2i. What is the other root?

Michael J.

A cubic equation can only have at most 3 roots.  You already have 3 roots.
 
x = 3      ,       x = -2i     , and         x = 2i
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05/14/17

Gary M.

tutor
Is there possibly a typo in the equation? Assuming that the given roots are meant to be 3+2i and 3-2i, it should be noted that neither of those are actual roots of the given equation.
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05/14/17

1 Expert Answer

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Michael J. answered • 05/14/17

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Move all terms to the left side of the equation.  This will make the right side equal to zero.
 
x3 - 5x2 + 7x - 7 = 0
 
 
Noticing that synthetic division and group factoring does not serve well to completely factor the left side, we use the graphing calculator to find the zeros.
 
Enter the function                   y = x3 - 5x2 + 7x - 7
 
Then press 2ND and TRACE.  Select the option "zero" and press ENTER.  It will ask you for your left and right bounds.  Pick them, and the calculator will give you an x coordinate on the bottom of the screen when y=0.  That x coordinate is your root.
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