SOLUTION: 3x^2-6x+c=0 what value of c will the equation have one rational root

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Question 952836: 3x^2-6x+c=0 what value of c will the equation have one rational root
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In order to have 1 rational root, you have
to make +sqrt%28+b%5E2-4%2Aa%2Ac+%29+=+0+ in
the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
-----------------------------------
+3x%5E2+-+6x+%2B+c+=+0+
+a+=+3+
+b+=+-6+
+c+=+c+
+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29+=+0+
+sqrt%28+%28-6%29%5E2+-+4%2A3%2Ac+%29+=+0+
+sqrt%28+36+-+12c+%29+=+0+
+36+-+12c+=+0+
+12c+=+36+
+c+=+3+
The equation for finding the roots is:
+3x%5E2+-+6x+%2B+3+=+0+
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-3%2C+10%2C+3x%5E2+-+6x+%2B+3+%29+
As you can see, it touches the x-axis in one place,
meaning 1 rational root