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# Finding Zero

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### Finding Zero

1. 1. Finding the Zeros<br />By Matt Selby<br />
2. 2. Step One<br />Start with your equation. Let’s say,<br /> f(x)= x^3 – 6x^2 + 13x- 10 for example. <br />
3. 3. Step Two<br />The next step is to use synthetic division. <br />x^3 – 6x^2 + 13x- 10 <br /> _l 1 -6 13 -10<br />In order to determine what number to divide by, we type the function into a calculator and look at the graph. <br />In this situation, the line seems to cross at the 2 mark (2,0). <br />
4. 4. Step 3<br />Next, insert the number into the synthetic division. <br />2 l 1 -6 13 -10 <br /> l +2 -8 10<br /> 1 -4 5 0<br />So we’re left with, 1x^2 -4x +5 <br />
5. 5. Step 3 <br />Now we take what was left, 1x^2 -4x +5 , and use quadratic formula. <br />(x = -b + or – radical(b^2) – 4 ac) / 2a <br />A= 1<br />B=-4<br />C= 5<br />
6. 6. Step 3 (cont.) <br />X= -(-4) + or – Radical ((-4)^2 – 4(1)(5) ) / 2(1)<br />Which becomes, 4 + or – radical (-4) /2<br />Which then simplifies to become, <br />4 + or – 2i/ 2 <br />This simplifies to 2 + or – i<br />
7. 7. Step 4 <br />So the zeros are 2 + or – i<br />When we convert them into f(x), they go in as opposites. <br />F(x)= ( x – 2) ( x – 2 +i)(x – 2- i) <br />
8. 8. Finish<br />That’s basically all is takes to find the zeros. It’s a fairly simple concept, the trick is knowing all the other equations that are used. <br />The end<br />