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How to powerpoint on finding all the zeros of a function!

How to powerpoint on finding all the zeros of a function!

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  • 1. Finding all of the zeros of a function
    By: Ashley Ezell
  • 2. 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
  • 3. 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
  • 4. 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
  • 5. Step 3Identify Zero’s
    2 ± i, 2
    F(x)= (x-2)(x-2+i)(x-2-i)
    ↑ ↑ ↑
    Opposite sign!
    GRAPH!!!