SOLUTION: Use the quadratic formula to solve the following equation. 3x^2-2x+1=0

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Question 93575: Use the quadratic formula to solve the following equation.
3x^2-2x+1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 3%2Ax%5E2-2%2Ax%2B1=0 ( notice a=3, b=-2, and c=1)

x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29 Plug in a=3, b=-2, and c=1



x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29 Negate -2 to get 2



x+=+%282+%2B-+sqrt%28+4-4%2A3%2A1+%29%29%2F%282%2A3%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)



x+=+%282+%2B-+sqrt%28+4%2B-12+%29%29%2F%282%2A3%29 Multiply -4%2A1%2A3 to get -12



x+=+%282+%2B-+sqrt%28+-8+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%282+%2B-+2%2Ai%2Asqrt%282%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%282+%2B-+2%2Ai%2Asqrt%282%29%29%2F%286%29 Multiply 2 and 3 to get 6



After simplifying, the quadratic has roots of

x=1%2F3+%2B+sqrt%282%29%2F3%2Ai or x=1%2F3+-+sqrt%282%29%2F3%2Ai

Notice if we graph the quadratic y=3%2Ax%5E2-2%2Ax%2B1, we get

graph of y=3%2Ax%5E2-2%2Ax%2B1

And we can see that there are no real roots

To visually verify the answer, check out this page to see a visual representation of imaginary roots