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Finding all of the zeros of a function By: Ashley Ezell
Step One Factor the function with synthetic division F(x)=X3-6x2+11x-6 1_| 1 -6 11 -6 1 -5 6 1 -5 6 0 F(x)= 1x2-5x+6
Step Two Do a diamond/box problem to factor this function Diamond of 6x2 at the top and -5x on the bottom is -3x and -2x When you plug these numbers in the box you get x-3 and x-2, set these equal to zero and they become positive
Step Two cont. An easier way to do this step is to use the quadratic formula-Only if function is set up as ax2+bx+c Ex. X2-4x+5 Quadratic formula: X= -b±√(b)2-4(a)(c) 2(a) -(-4) ±√(-4)2-4(1)(5) = 4 ± √-4 2(1) 2 simplify: 2 ± i