How do you write a polynomial in standard form given zeros 1 and 2 + 3i?

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How do you write a polynomial in standard form given zeros 1 and 2 + 3i?

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Answer 1 · 2016-07-15T17:33:45

$x^{2} - (3 + 3 i) x + (2 + 3 i)$ $x^2-(3+3i)x+(2+3i)$

Explanation:

A zero, say $a$ $a$ of a polynomial $f (x)$ $f(x)$ is one for which $f (a) = 0$ $f(a)=0$ .

Let us assume that zeros are ${a, b, c, d}$ ${a,b,c,d}$ , then it is apparent that such a polynomial could be $(x - a) (x - b) (x - c) (x - d)$ $(x-a)(x-b)(x-c)(x-d)$ .

As we need to write a polynomial with zeros $1$ $1$ and $2 + 3 i$ $2+3i$ , the polynomial is

$(x - 1) (x - 2 - 3 i)$ $(x-1)(x-2-3i)$ or

$x (x - 2 - 3 i) - 1 (x - 2 - 3 i)$ $x(x-2-3i)-1(x-2-3i)$ or

$x^{2} - 2 x - 3 i x - x + 2 + 3 i$ $x^2-2x-3ix-x+2+3i$ or

$x^{2} - 3 x - 3 i x + 2 + 3 i$ $x^2-3x-3ix+2+3i$ or

$x^{2} - (3 + 3 i) x + (2 + 3 i)$ $x^2-(3+3i)x+(2+3i)$

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How do you write a polynomial in standard form given zeros 1 and 2 + 3i?

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