anonymous
  • anonymous
any help would be appreciated.. I have a test, and I am unsure of my probs below... ty.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
where are the problems?
anonymous
  • anonymous
I have one... Given that the polynomial f(x) has a zero at x=2 find the remaining zeros.. f(x)=x^3-10x^2+41x-50
nowhereman
  • nowhereman
You can factor (x-2) from f(x) if it has a zero at x=2.

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anonymous
  • anonymous
What does that mean? It says my answer should be in a+bi form?
anonymous
  • anonymous
having a zero at x=2 means that (x-2) is one factor of f(x), you have to find the other factors.. using long division gives: \[f(x)=(x-2)(x^2-8x+25)=0\] you already have the solution x=2 to find the other solutions solve the quadratic equation: \[x^2-8x+25=0\]
anonymous
  • anonymous
using the quadratic formula gives us the two remaining solutions: \[x=4-3i, x=4+3i\]
anonymous
  • anonymous
do you know how to use the quadratic formula?
anonymous
  • anonymous
Long division.. we are being taught syntheic.. is that ok?
nowhereman
  • nowhereman
there is only one solution to that division, and that step is really trivial it does not matter how you solve it.
anonymous
  • anonymous
Can you show me the way the quadratic formula is worked out on here??
nowhereman
  • nowhereman
The solution formula for \[ x^2 + px + q = 0\] is \[x = -\frac{p}{2} \pm \sqrt{\frac{p^2}{4} - q}\]
anonymous
  • anonymous
And thats the quadratic formula??
anonymous
  • anonymous
becasue I have never seen that before??
nowhereman
  • nowhereman
Some schools teach the form \[ax^2 + bx +c = 0\] where you would of course get a formula which is a bit different. But the above is the exact solution formula for such quadratic problems.
anonymous
  • anonymous
Thanks

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