Question 267203
{{{h(x)=x^4-15x^3+70x^2-70x-156}}}
first we use a technique called P-N-I This gives us the positive negative and imaginary zero combinations
P . . . N . . . I
3 . . . 1 . . . 0
1 . . . .1 . . . 2
So, I see that we must have 1 negative root somewhere.
Next I apply synthetic division to get roots.
-1 // 1 . . . . -15 . . . . 70 . . . . -70 . . . . -156
 . . . . . . . . . . .-1 . . . . 16 . . . . .-86 . . . . 156
 . . . . .1 . . . . .-16 . . . 86 . . . . .-156 . . . .0
and then
6// 1 . . . . -16 . . . . 86 . . . . -156 
 . . . . . . . . . . 6 . . . . -60 . . . .156
 . . . . .1 . . . -10 . . . 26 . . . . .0
So we know that -1 and 6 are roots.
Now we can factor x^2 - 10x + 26 using the quadratic as
{{{x = (10 +- sqrt( 100-4*1*26 ))/(2) }}}
and then
{{{x = (10 +- sqrt(-4))/(2) }}}
which gives us imaginary answers of
{{{x = (5 +- i) }}}
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So, in total we have the following roots:
-6, 6, and 5 +-i