How do you write a polynomial in standard form given zeros $-2$ and $1 + 2i$ ?

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Answer 1 · 2016-09-01T02:33:19

The desired polynomial is
$x^2+(1-2i)x-2-4i$

If $a$ , $b$ and $c$ are the zeros of a polynomial, then the polynomial is

$(x-a)(x-b)(x-c)$ .

Hence, the polynomial with zeros as $-2$ and $1+2i$ will be

$(x-(-2))(x-(1+2i))$ or

$(x+2)(x-1-2i)$ or

$x(x-1-2i)+2(x-1-2i)$ or

$x^2-x-2ix+2x-2-4i$ or

$x^2+x-2ix-2-4i$ or

$x^2+(1-2i)x-2-4i$

How do you write a polynomial in standard form given zeros -2-2 and 1 + 2i1 + 2i?