SOLUTION: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state. 3x^2 + x - 3 = 0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state. 3x^2 + x - 3 = 0      Log On


   

Question 247824: Use the quadratic formula to solve the euation. If the equation has no real number solutions, so state.
3x^2 + x - 3 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2 + x - 3 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B1x%2B-3+=+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=%281%29%5E2-4%2A3%2A-3=37.

Discriminant d=37 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+37+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+37+%29%29%2F2%5C3+=+0.847127088383037
x%5B2%5D+=+%28-%281%29-sqrt%28+37+%29%29%2F2%5C3+=+-1.18046042171637

Quadratic expression 3x%5E2%2B1x%2B-3 can be factored:
3x%5E2%2B1x%2B-3+=+%28x-0.847127088383037%29%2A%28x--1.18046042171637%29
Again, the answer is: 0.847127088383037, -1.18046042171637. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B1%2Ax%2B-3+%29