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

Question

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

1 Answer

Impact of this question

4253 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-02T09:49:15

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

Explanation:

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

Now, we can establish the sign chart

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

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

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

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

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

Therefore,

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

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

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