How do you solve $(x+5)(x-2)>=0$ ?

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Answer 1 · 2016-12-20T15:40:20

The answer is $x in ] -oo,-5 ] uu [2, +oo[$

Let $f(x)=(x+5)(x-2)$

Now, we can do a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5$ $color(white)(aaaa)$ $2$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+5$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

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

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

Therefore,

$f(x)>=0$ , when $x in ] -oo,-5 ] uu [2, +oo[$

graph{(x+5)(x-2) [-28.86, 28.85, -14.43, 14.43]}

How do you solve (x+5)(x-2)>=0(x+5)(x-2)>=0?