anonymous
  • anonymous
Find a cubic function with the given zeros. √2, -√2, -2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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dape
  • dape
First write the function in terms of it factors, since you know it's zeros, so you have \[(x-\sqrt{2})(x-a)(x-b)=?\] Where a and b are the second and third root, then just expand this and you will have your function.
anonymous
  • anonymous
Can you help me expand it ?
dape
  • dape
You can try it first and I'll check if you did it right

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dape
  • dape
So to be clear \(a=-\sqrt{2}\) (the second root) and \(b=-2\) (the third root).
anonymous
  • anonymous
x^3 - bx^2 -ax^2 +abx - sqrt(2)x^2 + sqrt(2)bx + sqrt(2)ax - sqrt(2)ab ? @dape
dape
  • dape
Let's see.
dape
  • dape
You should put in the zeros for \(a\) and \(b\), the first thing I wrote was just an example.
dape
  • dape
In general you would have (x-a)(x-b)(x-c), but here you know the three zeros a, b and c, so you should use those numbers instead of the symbols.
dape
  • dape
So a function with the given zeros are \(f(x)=(x-\sqrt{2})(x+\sqrt{2})(x+2)\), since if you put in \(x=\pm\sqrt{2}\) or \(x=-2\) you get zero. So you should expand this thing to get the (same) function with \(x^3\)'s in it.

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