SOLUTION: please help use the quadratic formula x= -b+ (small dash under plus sign)sqrt (b^2-4ac)/2a find the roots of the equation x^2-4/3x+1/3=0

Question 140894: please help use the quadratic formula x= -b+ (small dash under plus sign)sqrt (b^2-4ac)/2a find the roots of the equation x^2-4/3x+1/3=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Multiply both sides by the LCD 3. This will cancel out the denominators and clear the fractions

Distribute and multiply

Now 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=-4, and c=1

Negate -4 to get 4

Square -4 to get 16 (note: remember when you square -4, 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

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

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