How do you find all the zeros of $f (x) = x^{4} - x^{3} - 20 x^{2}$ $f(x)=x^4 - x^3 - 20x^2$ ?

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How do you find all the zeros of $f (x) = x^{4} - x^{3} - 20 x^{2}$ $f(x)=x^4 - x^3 - 20x^2$ ?

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Answer 1 · 2016-02-27T19:40:24

Factor $f (x) = x^{2} (x - 5) (x + 4)$ $f(x) = x^2(x-5)(x+4)$ , hence find zeros:

$x = 0$ $x=0$ (twice), $x = 5$ $x=5$ and $x = - 4$ $x=-4$

Explanation:

Separate out the common factor $x^{2}$ $x^2$ of the terms, then factor the remaining quadratic using $5 \times 4 = 20$ $5 xx 4 = 20$ and $5 - 4 = 1$ $5 - 4 = 1$ as follows:

$f (x) = x^{4} - x^{3} - 20 x^{2}$ $f(x) = x^4-x^3-20x^2$

$= x^{2} (x^{2} - x - 20)$ $=x^2(x^2-x-20)$

$= x^{2} (x - 5) (x + 4)$ $=x^2(x-5)(x+4)$

Hence zeros: $x = 0$ $x=0$ (twice), $x = 5$ $x=5$ and $x = - 4$ $x=-4$

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How do you find all the zeros of $f (x) = x^{4} - x^{3} - 20 x^{2}$ $f(x)=x^4 - x^3 - 20x^2$ ?

1 Answer

Explanation:

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How do you find all the zeros of $f (x) = x^{4} - x^{3} - 20 x^{2}$ $f(x)=x^4 - x^3 - 20x^2$ ?