+69 One of the roots of 2x 3 − 9x 2 + 13x + k = 0 is x = 2. Find the other two roots.
+129903
Performing some synthetic division
2 [ 2 -9 13 k ]
4 -10 6
______________________
2 -5 3 k + 6
So
k + 6 = 0
k = -6
So.....
2 [ 2 -9 13 - 6 ]
4 -10 6
___________________________
2 -5 3 0
The remaining polynomial is
2x^2 - 5x + 3 = 0
(2x - 3) (x - 1) = 0
Set each factor to 0 and solve for x and we get that the other two roots are
x = 3/2 and x = 1
