Finding a polynomial of a given degree with given zeros

label Algebra
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Find a polynomial f(x) of degree 4 with real coeffiecients and the following zeros. 

4, -3, -1+i

Simplify completely. 

Oct 16th, 2015

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The zeros of f(x) are 

x = 4, x = -3 and x = -1+i


So factors of f(x) are

x - 4,   x + 3,  x - (-1 + i) , x - (-1 - i)  

(because if complex roots or zeros always occur in conjugate pairs. So if -1 + i is a root then its complex conjugate -1 - i is also a root of f(x))

 Now multiply these four factors to get the polynomial.



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Oct 16th, 2015

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