cant figure this out

A

aidan

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Dec 4, 2019
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How do I find a polynomial function of least degree having only real coefficients , a leading coefficient of 1, and roots of 1- square root 3, 1+ square root 3, and 7-i The polynomial function is P(x) =. Simplify answer
 
Hello, and welcome to FMH! :)

Your polynomial is going to have one root not listed...can you state that root?
 
thats the point that I am stuck at, I just cannot remember what to do once I have all of the roots
 
aidan said:
thats the point that I am stuck at, I just cannot remember what to do once I have all of the roots
Click to expand...

Hint:

[MATH]P(x)=\prod_{k=1}^4(x-r_k)=(x-r_1)(x-r_2)(x-r_3)(x-r_4)[/MATH]
 
Suppose x= 7 is a root of a polynomial, P(x). Please assume that 7* means any number BUT 7.

Assume P(x) = (x-7*)(x-7*)(x-7*)...(x-7*). Will P(7) = 0? Why not? What must a factor of P(x) be so that P(7)=0?
 
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