SOLUTION: Which of the following are solutions to the equation below? Check all that apply. 3x2 - 5x + 1 = 0 A. x = -5 - square root of 13 over 6 B. x = 5 - square root of 37

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Which of the following are solutions to the equation below? Check all that apply. 3x2 - 5x + 1 = 0 A. x = -5 - square root of 13 over 6 B. x = 5 - square root of 37      Log On

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Question 304532: Which of the following are solutions to the equation below?
Check all that apply.
3x2 - 5x + 1 = 0
A. x = -5 - square root of 13 over 6
B. x = 5 - square root of 37 over 6
C. x = 5 + square root of 13 over 6
D. x = 5 - square root of 13 over 6
E. x = 5 + square root of 37 over 6
F. x = -5 + square root of 13 over 6

Answer by vleith(2825) About Me  (Show Source):
You can put this solution on YOUR website!
Go to this URL and use it to help you solve this problem. It is a nice tool to keep in your bookmarks
http://www.algebra.com/algebra/homework/quadratic/quadratic.solver

I used that URL using your coefficients to get this result
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-5x%2B1+=+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=%28-5%29%5E2-4%2A3%2A1=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+13+%29%29%2F2%5C3+=+1.43425854591066
x%5B2%5D+=+%28-%28-5%29-sqrt%28+13+%29%29%2F2%5C3+=+0.232408120756002

Quadratic expression 3x%5E2%2B-5x%2B1 can be factored:
3x%5E2%2B-5x%2B1+=+3%28x-1.43425854591066%29%2A%28x-0.232408120756002%29
Again, the answer is: 1.43425854591066, 0.232408120756002. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-5%2Ax%2B1+%29