SOLUTION: I'm having some trouble with a question on my test: . -11x^2+12x - 6 = 0 . Answers: . A) x ={-6 +- i[SQRT(60)]}/11 B) x = {-6 +- i[SQRT(30)]}/-11 C) x = {6 +- i[SQRT(12)]

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I'm having some trouble with a question on my test: . -11x^2+12x - 6 = 0 . Answers: . A) x ={-6 +- i[SQRT(60)]}/11 B) x = {-6 +- i[SQRT(30)]}/-11 C) x = {6 +- i[SQRT(12)]      Log On


   

Question 744694: I'm having some trouble with a question on my test:
.
-11x^2+12x - 6 = 0
.
Answers:
.
A) x ={-6 +- i[SQRT(60)]}/11
B) x = {-6 +- i[SQRT(30)]}/-11
C) x = {6 +- i[SQRT(12)]}/6
D) x = {-6 +- i[SQRT(22)]}/-11
E) x = {-11 +- i} /6
F) x = {11 +- i} /-6
.
.
What I did first is to insert the question into the quadratic formula, with -11, 12 and -6 as a, b and c.
(-12 ± √144 - 264) / (-22)
Which turns into
(-12±√-120) / -22
.
But now I'm stuck. Could I have some help please?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
-11x^2+12x - 6 = 0
.
Answers:
.
A) x ={-6 +- i[SQRT(60)]}/11
B) x = {-6 +- i[SQRT(30)]}/-11
C) x = {6 +- i[SQRT(12)]}/6
D) x = {-6 +- i[SQRT(22)]}/-11
E) x = {-11 +- i} /6
F) x = {11 +- i} /-6
.
.
What I did first is to insert the question into the quadratic formula, with -11, 12 and -6 as a, b and c.
(-12 ± √144 - 264) / (-22)
Which turns into
(-12±√-120) / -22
.
But now I'm stuck. Could I have some help please?
-----------------------
(-12±√-120) / -22 You were almost done.
= %286+%2B+i%2Asqrt%2830%29%29%2F11
= %286+-+i%2Asqrt%2830%29%29%2F11
--> C
============
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -11x%5E2%2B12x%2B-6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A-11%2A-6=-120.

The discriminant -120 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -120 is + or - sqrt%28+120%29+=+10.9544511501033.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-11%2Ax%5E2%2B12%2Ax%2B-6+%29