How do you write a polynomial in standard form given the zeros (5 ,+i√3 , -i√3)?

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How do you write a polynomial in standard form given the zeros (5 ,+i√3 , -i√3)?

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Answer 1 · 2016-03-25T09:29:48

$f (x)) = x^{3} - 5 x^{2} + 9 x - 45$ $f(x))=x^3-5x^2+9x-45$

Explanation:

A polynomial with zeros ${a, b, c}$ ${a,b,c}$ is given by $f (x) = (x - a) (x - b) (x - c)$ $f(x)=(x-a)(x-b)(x-c)$ .

As the zeros are ${5, + i \sqrt{3}, - i \sqrt{3}}$ ${5,+isqrt3,-isqrt3}$ ,

$f (x) = (x - 5) (x - i \sqrt{3}) (x - (- i \sqrt{3})) = (x - 5) (x - i \sqrt{3}) (x + i \sqrt{3})$ $f(x)=(x-5)(x-isqrt3)(x-(-isqrt3))=(x-5)(x-isqrt3)(x+isqrt3)$ or

$f (x) = (x - 5) (x^{2} - {(i \sqrt{3})}^{2})$ $f(x)=(x-5)(x^2-(isqrt3)^2)$ or

$f (x) = (x - 5) (x^{2} - (- 9)) = (x - 5) (x^{2} + 9)$ $f(x)=(x-5)(x^2-(-9))=(x-5)(x^2+9)$ or

$f (x) = x (x^{2} + 9) - 5 (x^{2} + 9) = x^{3} + 9 x - 5 x^{2} - 45$ $f(x)=x(x^2+9)-5(x^2+9)=x^3+9x-5x^2-45$ or

$f (x)) = x^{3} - 5 x^{2} + 9 x - 45$ $f(x))=x^3-5x^2+9x-45$

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How do you write a polynomial in standard form given the zeros (5 ,+i√3 , -i√3)?

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