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NotSoSmart  Dec 4, 2017
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7.

y  =  ( x + 8)^3  +  9     shifts the parent function - x^3 -  to the left 8 units and up 3 units

The parent function  has only one real zero  and this translated function also has  one real zero

8.  If we can add the coefficients and constant  and get 0,, then 1 is a root

So....in the first one    -1 -6 + 6 - 6 + 5  =  -2   .....so it isn't this one

Look at the second one  1 + 6 - 6 + 6 - 5 = 2   not this one either

Look at the last one   x^4 - 6x^3 + 6x^2 - 6x + 5

We can write    x^4 - 6x^3 + 5x^2 + x^2 -6x + 5

Factor as    x^2(x^2 - 6x + 5)  + 1 (x^2 - 6x + 5)

(x^2 + 1) ( x^2 - 6x + 5)

(x^2 + 1) (x - 5) ( x - 1)

Notice that if we set the last two factors to 0  and solve for x....we get that x = 5  and x  = 1

And these are the two  zeroes.......so...the last one is correct

9.

If  -1 + 4i  and -1 - 4i  are roots....we have that

[ x - (-1 + 4i) ]  [ x - (-1 - 4i) ]  = 0        expand this, NSS....watch the math!!!

[ x^2 - x (- 1 + 4i) - x(-1 - 4i)  + (-1 + 4i) (-1 - 4i)  ]  = 0

[ x^2  + x - 4xi  + x + 4xi  +  ( 1 + 4i - 4i - 16i^2 ]  = 0

Remember that  {  -16i^2  =  -16 * -1  = 16  }

[ x^2  +  2x  +  1 +  16 ]  = 0

[ x^2 + 2x  + 17 ]  =  0

CPhill  Dec 4, 2017

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