How do you solve $x^2+2x-15<=0$ using a sign chart?

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Answer 1 · 2016-12-18T08:11:25

The answer is $x in [-5,3]$

Let $f(x)=x^2+2x-15=(x-3)(x+5)$

Let's do the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5$ $color(white)(aaaa)$ $3$ $color(white)(aaaa)$ $+oo$

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

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

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

So,

$f(x<=0)$ when $x in [-5,3]$

How do you solve x^2+2x-15<=0x^2+2x-15<=0 using a sign chart?