Which of the following is the complete list of roots for the polynomial function f (x) = (x2 + 6x + 8) (x2 + 6x + 13)?

-2, -4, -3 + 2i, -3-2i

Step-by-step explanation:

Equaling the function to zero we have:

(x ^ 2 + 6x + 8) (x ^ 2 + 6x + 13) = 0  

For the first parenthesis we have:

(x ^ 2 + 6x + 8) = 0\\(x + 4) (x + 2) = 0  

Therefore the roots are:

x = - 4\\x = - 2  

For the second parenthesis we have:

(x ^ 2 + 6x + 13) = 0  

By completing squares we have:

x ^ 2 + 6x = -13  

x ^ 2 + 6x + (\frac{6}{2}) ^ 2 = -13 + (\frac{6}{2}) ^ 2\\x ^ 2 + 6x + 9 = -13 + 9\\(x + 3) ^ 2 = - 4\\x + 3 = +/- \sqrt{-4}    

Therefore the roots are:

x = -3 + 2i\\x = -3 - 2i  

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2