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Help please.

 Dec 4, 2017
 #1
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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

 

So....the answer is  1

 

 

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

 

 

cool cool cool

 Dec 4, 2017

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