SOLUTION: Find the discriminant of the equation 6x-9x^{2}+8 = 0

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Question 902673: Find the discriminant of the equation 6x-9x^{2}+8 = 0
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: 6X+-+9X%5E2+%2B+8+=+0
I am going to rewrite the equation in standard form.
-9X%5E2+%2B+6X+%2B+8+=+0
To find the discriminant, use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case -9X%5E2%2B6X%2B8+=+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=%286%29%5E2-4%2A-9%2A8=324.

Discriminant d=324 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+324+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%286%29%2Bsqrt%28+324+%29%29%2F2%5C-9+=+-0.666666666666667
X%5B2%5D+=+%28-%286%29-sqrt%28+324+%29%29%2F2%5C-9+=+1.33333333333333

Quadratic expression -9X%5E2%2B6X%2B8 can be factored:
-9X%5E2%2B6X%2B8+=+-9%28X--0.666666666666667%29%2A%28X-1.33333333333333%29
Again, the answer is: -0.666666666666667, 1.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-9%2Ax%5E2%2B6%2Ax%2B8+%29


The discriminant is 324