SOLUTION: Can someone please help me with my homework? Thanks :D 1.What if I have +√3 and -√3 as the roots. What is the equation? 2. Graph the equation in a sign graph: x^2+8x-

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please help me with my homework? Thanks :D 1.What if I have +√3 and -√3 as the roots. What is the equation? 2. Graph the equation in a sign graph: x^2+8x-      Log On


   

Question 982479: Can someone please help me with my homework? Thanks :D
1.What if I have +√3 and -√3 as the roots. What is the equation?
2. Graph the equation in a sign graph: x^2+8x-7=0
In question no. 2, I find the roots of it first. Since it's not a perfect square trinomial, and 8 is an even number, I used completing the square.
x^2+8x=7
x^2+8x+(8/2)^2=7+(8/2)^2
x^2+8x+16=23
x^2+8x+16-23=0
x^2+8x-7=0
But i ended up returning to the original equation :/
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+8x=7
x^2+8x+(8/2)^2=7+(8/2)^2
x^2+8x+16=23
x^2+8x+16=23
(x+4)^2 = 23
(x+4) = +/-sqrt(23)
x= -4 +/- sqrt(23)

sum of roots = 0
product of roots = -3
x^2-(sum of roots)x+(product of roots =0
x^2-3=0 is the equation

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

1.  What if I have  sqrt%283%29  and  -sqrt%283%29  as the roots.  What is the equation?

The equation is  x%5E2-3 = 0,  or  (which is the same)  x%5E2 = 3.

2.  In question no. 2

See how completing the square works.

x%5E2%2B8x = 7,

%28x+%2B+%288%2F2%29%29%5E2 - %288%2F2%29%5E2 = 7,

%28x+%2B+4%29%5E2 - 4%5E2 = 7,

%28x+%2B+4%29%5E2 - 16 = 7,

%28x+%2B+4%29%5E2 = 7 + 16,

%28x+%2B+4%29%5E2 = 23,

x+%2B+4 = +/- sqrt%2823%29,

x = -4 +/- sqrt%2823%29.