How do you write a polynomial with zeros: 0, 2, 5?

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How do you write a polynomial with zeros: 0, 2, 5?

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Answer 1 · 2016-02-05T10:08:37

$x^{3} - 7 x^{2} + 10 x$ $x^3-7x^2+10x$

Explanation:

A polynomial has a zero at a point $a$ $a$ if $(x - a)$ $(x-a)$ is a factor of the polynomial. Then, to create a polynomial with certain desired roots, we simply multiply the desired factors. In this case, that gives us

$(x - 0) (x - 2) (x - 5) = x (x - 2) (x - 5)$ $(x-0)(x-2)(x-5) = x(x-2)(x-5)$

$= x (x^{2} - 7 x + 10)$ $=x(x^2-7x+10)$

$= x^{3} - 7 x^{2} + 10 x$ $=x^3-7x^2+10x$

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How do you write a polynomial with zeros: 0, 2, 5?

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