How do you solve $(x-1)(x-2)(x-3)>=0$ using a sign chart?

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How do you solve $(x-1)(x-2)(x-3)>=0$ using a sign chart?

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Answer 1 · 2017-01-02T09:49:15

The answer is $x in [1 ,2 ] uu [3, +oo [$

Explanation:

Let $f(x)=(x-1)(x-2)(x-3)$

Now, we can establish the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $1$ $color(white)(aaaaaa)$ $2$ $color(white)(aaaaaaa)$ $3$ $color(white)(aaaaaa)$ $-oo$

$color(white)(aaaa)$ $x-1$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x-2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $x-3$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$

Therefore,

$f(x)>=0$ when $x in [1 ,2 ] uu [3, +oo [$

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How do you solve $(x-1)(x-2)(x-3)>=0$ using a sign chart?

1 Answer

Explanation:

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How do you solve (x-1)(x-2)(x-3)>=0(x-1)(x-2)(x-3)>=0 using a sign chart?

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How do you solve $(x-1)(x-2)(x-3)>=0$ using a sign chart?