How do you solve $m^{3} - 2 m^{2} - 15 m > 0$ $m^3-2m^2-15m>0$ using a sign chart?

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How do you solve $m^{3} - 2 m^{2} - 15 m > 0$ $m^3-2m^2-15m>0$ using a sign chart?

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Answer 1 · 2017-03-06T16:01:33

The solution is $m \in] - 3, 0 [\cup] 5, + \infty [$ $m in ]-3,0 [uu]5, +oo[$

Explanation:

Let's factorise the inequality

$m^{3} - 2 m^{2} - 15 m > 0$ $m^3-2m^2-15m>0$

$m (m^{2} - 2 m - 15) > 0$ $m(m^2-2m-15)>0$

$m (m + 3) (m - 5) > 0$ $m(m+3)(m-5)>0$

Let $f (m) = m (m + 3) (m - 5)$ $f(m)=m(m+3)(m-5)$

Now, we can build the sign chart

$a a a a$ $color(white)(aaaa)$ $m$ $m$ $a a a a$ $color(white)(aaaa)$ $- \infty$ $-oo$ $a a a a$ $color(white)(aaaa)$ $- 3$ $-3$ $a a a a$ $color(white)(aaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $5$ $5$ $a a a a a$ $color(white)(aaaaa)$ $+ \infty$ $+oo$

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

$a a a a$ $color(white)(aaaa)$ $m$ $m$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $+$ $+$

$a a a a$ $color(white)(aaaa)$ $m - 5$ $m-5$ $a a a a a$ $color(white)(aaaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$

$a a a a$ $color(white)(aaaa)$ $f (m)$ $f(m)$ $a a a a a a$ $color(white)(aaaaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$ $a a a a$ $color(white)(aaaa)$ $-$ $-$ $a a a a$ $color(white)(aaaa)$ $+$ $+$

Therefore,

$f (m) > 0$ $f(m)>0$ , when $m \in] - 3, 0 [\cup] 5, + \infty [$ $m in ]-3,0 [uu]5, +oo[$

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How do you solve $m^{3} - 2 m^{2} - 15 m > 0$ $m^3-2m^2-15m>0$ using a sign chart?

1 Answer

Explanation:

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How do you solve m^3-2m^2-15m>0m3−2m2−15m>0m^3-2m^2-15m>0 using a sign chart?

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How do you solve $m^{3} - 2 m^{2} - 15 m > 0$ $m^3-2m^2-15m>0$ using a sign chart?