Finding zeros
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The document discusses finding the zeros of a polynomial function. It explains that to find the zeros, one graphs the function to identify possible zeros, then uses synthetic division to divide the polynomial into linear and quadratic factors. For the given polynomial, synthetic division could only be performed once, indicating there are three distinct real zeros at x=0, x=-3, and x=-3. However, since the quadratic formula could not be applied, this particular polynomial does not have a double zero, showing that some problems cannot be solved as initially indicated.
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- 1. Finding Zeros Ashley H
- 2. You begin of course with a function: F(x)= x + 6x + 10x + 6x + 9 you then graph the function (optional) this helps you spot the points at which it hits the X-axis it seems to cross exactly at three now we have to do some digging Start 2 4 3
- 3. Now you have to synthetically divide first take out all the real numbers and put them in a line don’t forget if your 1 6 10 6 9 -3 -9 -3 -9 1 3 1 3 0 But we need to divide again to attempt the quadratic formula! you can’t do the quadratic formula!! Digging? -3 Missinga number place zero in it’s place! _________________________ BUT THE LINE DOESN’T CROSS TWICE?! it doesn’t
- 4. So some problems can’t be possible So if it can’t divide again Or you can’t use the quadratic formula You may have that special problem that you can just say “no…” (I don’t think I picked a good problem) <D