How do you solve $t^3-13t-12=0$ ?

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Answer 1 · 2016-12-22T20:25:44

The solutions are $t=-1$ , $t=4$ and $t=-3$ .

Given:

$f(t) = t^3-13t-12$

Notice that $12+1=13$ , so is there some value like $t=+-1$ which will give $f(t) = 0$ ?

We find:

$f(-1) = -1+13-12 = 0$

So $t=-1$ is a zero and $(t+1)$ a factor:

$t^3-13t-12 = (t+1)(t^2-t-12)$

To factor $t^2-t-12$ find a pair of factors of $12$ which differ by $1$ .

The pair $4, 3$ works. Hence we find:

$t^2-t-12 = (t-4)(t+3)$

So the other two zeros are:

$t = 4" "$ and $" "t = -3$

How do you solve t^3-13t-12=0t^3-13t-12=0 ?