SOLUTION: I am working on this problem and believe I resolved half of the question but not the other half. 3x^2-6x+1=0 I found the discriminant of 24 But I need the number of real sol

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am working on this problem and believe I resolved half of the question but not the other half. 3x^2-6x+1=0 I found the discriminant of 24 But I need the number of real sol      Log On


   

Question 1049177: I am working on this problem and believe I resolved half of the question but not the other half.
3x^2-6x+1=0
I found the discriminant of 24 But I need the number of real solutions
Found 2 solutions by josmiceli, ewatrrr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+3x%5E2+-+6x+%2B+1+=+0+
The discriminant is:
+b%5E2+-+4a%2Ac+=+%28-6%29%5E2+-+4%2A3%2A1+
+b%5E2+-+4a%2Ac+=+36+-+12+
+b%5E2+-+4a%2Ac+=+24+
-----------------------
The roots are:
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
First I'll take the positive square root:
+x%5B1%5D+=+%28+-%28-6%29+%2B+sqrt%2824%29+%29+%2F+%282%2A3%29+
+x%5B1%5D+=+%28+6+%2B+2%2Asqrt%286%29+%29+%2F+6+
+x%5B1%5D+=+1+%2B+%281%2F3%29%2Asqrt%286%29+
------------------------------
Now taking the negative square root:
+x%5B2%5D+=+%28+6+-+sqrt%2824%29+%29+%2F+6+
+x%5B2%5D+=+1+-+%281%2F3%29%2Asqrt%286%29+
------------------------------
These are the 2 real roots
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+3x%5E2+-+6x+%2B+1+%29+

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
3x^2-6x+1=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%286+%2B-+sqrt%28+24%29%29%2F%286%29++=+%286+%2B-+sqrt%28+4%2A6%29%29%2F%286%29+
x+=+%286+%2B-+2sqrt%28+6%29%29%2F%286%29+
real solutions:
x+=+%281+%2B-+%281%2F3%29sqrt%28+6%29%29+
x = 1 + %281%2F3%29sqrt%28+6%29
0r
x = 1 - %281%2F3%29sqrt%28+6%29