Find zeroes of -2x4+5x3+4x-7?
When x=1, this becomes -2+5+4-7=0, so x-1 is a factor (x=1 is a zero).
Use synthetic division to divide by the zero:
1 | -2 5 0 4 -7
-2 -2 3 3 | 7
-2 3 3 7 | 0 = -2x3+3x2+3x+7.
The two graphs below show the original function in red and the above cubic function in blue. The red function intersects the x-axis at two points, one of which is x=1, the zero we found and the other is another zero, common to both functions at around x=2.6. A more accurate evaluation can be found using Newton's Iteration Method (not shown here). Using this method the zero is x=2.596715 to 6 dec places.
The remaining zeroes are complex numbers, which are -0.548358±1.023309i.
