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Each solution to x^2 + 5x + 8 = 0 can be written in the form x = a + b i, where a$ and $b are real numbers. What is a + b^2?

 

Rewrite the expression g^4 + 12g^2 + 9 in the form c(g^2 + p)^2 + q. What is q?

 May 29, 2019
 #1
avatar+106519 
+2

x^2 + 5x + 8  = 0      complete the square on x

 

x^2 + 5x + 25/4  = -8 + 25/4

 

(x + 5/2)^2  = -32/4 + 25/4

 

(x + 5/2)^2  =  -7/4     take both roots

 

(x + 5/2)  =  ± [ √7  / 2 ] i   subtract 5/2 from both sides

 

x =   -5/2 ±  [√7 / 2 ] i

 

a =-5/2  b^2  = 7/4

 

So

 

a + b^2  =  -5/2 + 7/4  =   -10/4 + 7/4  =   -3/4

 

cool cool cool

 May 29, 2019
 #2
avatar
+2

Thank you!

Guest May 29, 2019
edited by Guest  May 29, 2019
edited by Guest  May 29, 2019
 #3
avatar+106519 
+2

g^4 + 12g^2 + 9       complete the square

 

g^4 + 12g^2 + 36 + 9 - 36       simplify

 

(g^2 + 6)^2  -  27

 

q  =  - 27

 

 

cool cool cool

 May 29, 2019

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