How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?

1 Answer
José F.
Mar 12, 2016

When we know the zeros of a polynomial #z_i# , we can obtain the polynomial, by multiplying a constant different of zero, #a#, by the product of all #(x-z_i)#.

If zeros are # 1, -1, sqrt(3)i, -sqrt(3)i#

The polynomial will be:

#a(x-1)(x+1)(x-sqrt(3)i)(x+sqrt(3)i)#

#a(x^2-1)(x^2+3)#

#a(x^4+3x^2-x^2-3)#

#a(x^4+2x^2-3)#, where a is any real number except zero.

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