SOLUTION: Find a polynomial of minimum degree that has the given zeros: {{{11-sqrt(3)}}} and {{{11+sqrt(3)}}}.
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The polynomial is:
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Question 596017: Find a polynomial of minimum degree that has the given zeros: and .
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The polynomial is:
Found 2 solutions by math-vortex, richard1234:
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Find a polynomial of minimum degree that has the given zeros.
and .
Hi, there--
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Since we have two zeros here, the degree of the polynomial will be two at a minimum. In addition, every root corresponds to a factor of the polynomial. To find a polynomial, we take each root and turn it into a factor. Then, we multiply the factors together to give the polynomial. Let's write the polynomial in terms of x.
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If is a zero for our polynomial, then is a factor. Likewise, if is a zero for our polynomial, then is the other factor.
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So, our polynomial in factored form is
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We'll simplify, multiply this out using the distributive property, and combine like terms to get the polynomial into expanded form.
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I hope this helps! Feel free to email if any part of my explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
)(x - (11+\sqrt{3})))
We can also write this as
 + \sqrt{3})((x-11) - \sqrt{3}))
Applying the difference of two squares, this is equal to
^2 - 3)
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