SOLUTION: can you please help me use the quadratic formula to solve the following and leave irrational roots in the simplest radical form: (((3x^2-4x-5=0)))

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Question 179728This question is from textbook algebra structure and method
: can you please help me use the quadratic formula to solve the following and leave irrational roots in the simplest radical form: (((3x^2-4x-5=0))) This question is from textbook algebra structure and method

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2-4x-5=0
:
so: system%28x=%282%2F3%29%2Bsqrt%2876%29%2F6%2Cx=%282%2F3%29-sqrt%2876%29%2F6%29
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-4x%2B-5+=+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=%28-4%29%5E2-4%2A3%2A-5=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+76+%29%29%2F2%5C3+=+2.11963298118022
x%5B2%5D+=+%28-%28-4%29-sqrt%28+76+%29%29%2F2%5C3+=+-0.786299647846891

Quadratic expression 3x%5E2%2B-4x%2B-5 can be factored:
3x%5E2%2B-4x%2B-5+=+%28x-2.11963298118022%29%2A%28x--0.786299647846891%29
Again, the answer is: 2.11963298118022, -0.786299647846891. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-4%2Ax%2B-5+%29