SOLUTION: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer. 3x2 - 7x + 6 = 0

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Question 193767: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.
3x2 - 7x + 6 = 0


Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
in the equation ax%5E2%2Bbx%2Bc=0 the discriminant is D=b%5E2-4ac
:
%28-7%29%5E2-4%283%29%286%29=49-72=-23
:
since D<0 there are 2 complex solutions
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-7x%2B6+=+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=%28-7%29%5E2-4%2A3%2A6=-23.

The discriminant -23 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 -23 is + or - sqrt%28+23%29+=+4.79583152331272.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B6+%29