George has a quadratic of the form $x^2+bx+\frac13$, where $b$ is a specific negative number. Using his knowledge of how to complete the square, George is able to rewrite this quadratic in the form $(x+m)^2+\frac{1}{12}$. What is $b$?

Guest Jan 23, 2018

#1**+2 **

Best Answer

x^{2} + bx + 1/3

= x^{2} + bx + (b/2)^{2} - (b/2)^{2} + 1/3

= (x + b/2)^{2} - (b/2)^{2} + 1/3

Now we can see that...

-(b/2)^{2} + 1/3 = 1/12

-(b/2)^{2} = 1/12 - 1/3

-(b/2)^{2} = -1/4

(b/2)^{2} = 1/4

b^{2}/4 = 1/4

b^{2} = 1

b = ± 1

b is a negative number, so b = -1

hectictar
Jan 23, 2018