SOLUTION: Use the quadratic formula to solve the following quadratic equations
3x²- 2x + 1 =0
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Question 102549: Use the quadratic formula to solve the following quadratic equations
3x²- 2x + 1 =0
Answer by jim_thompson5910(35256) (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
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=3, b=-2, and c=1
Negate -2 to get 2
Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 3 to get 6
After simplifying, the quadratic has roots of
or
Notice if we graph the quadratic , we get
graph of
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
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