Answer: −
sqrt of -13 =−9.606
Step-by-step explanation: Root plot for : y = x2+12x+23
Axis of Symmetry (dashed) {x}={-6.00}
Vertex at {x,y} = {-6.00,-13.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-9.61, 0.00}
Root 2 at {x,y} = {-2.39, 0.00}
Solving x2+12x+23 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = 12
C = 23
Accordingly, B2 - 4AC =
144 - 92 =
52
Applying the quadratic formula :
-12 ± √ 52
x = ——————
2
Can √ 52 be simplified ?
Yes! The prime factorization of 52 is
2•2•13
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 52 = √ 2•2•13 =
± 2 • √ 13
√ 13 , rounded to 4 decimal digits, is 3.6056
So now we are looking at:
x = ( -12 ± 2 • 3.606 ) / 2
Two real solutions:
x =(-12+√52)/2=-6+√ 13 = -2.394
or:
x =(-12-√52)/2=-6-√ 13 = -9.606
