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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-%284%2F3%29x%2B1%2F3=0 Start with the given equation


3%28x%5E2-%284%2Fcross%283%29%29x%2B1%2Fcross%283%29%29=3%2A0 Multiply both sides by the LCD 3. This will cancel out the denominators and clear the fractions


3x%5E2-4x%2B1=0 Distribute and multiply


Now 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%5E2-4%2Ax%2B1=0 ( notice a=3, b=-4, and c=1)




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



x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A1+%29%29%2F%282%2A3%29 Negate -4 to get 4



x+=+%284+%2B-+sqrt%28+16-4%2A3%2A1+%29%29%2F%282%2A3%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)



x+=+%284+%2B-+sqrt%28+16%2B-12+%29%29%2F%282%2A3%29 Multiply -4%2A1%2A3 to get -12



x+=+%284+%2B-+sqrt%28+4+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%284+%2B-+2%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%284+%2B-+2%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%284+%2B+2%29%2F6 or x+=+%284+-+2%29%2F6

Lets look at the first part:

x=%284+%2B+2%29%2F6

x=6%2F6 Add the terms in the numerator
x=1 Divide

So one answer is
x=1



Now lets look at the second part:

x=%284+-+2%29%2F6

x=2%2F6 Subtract the terms in the numerator
x=1%2F3 Divide

So another answer is
x=1%2F3

So our solutions are:
x=1 or x=1%2F3

Notice when we graph 3%2Ax%5E2-4%2Ax%2B1, we get:

+graph%28+500%2C+500%2C+-9%2C+11%2C+-9%2C+11%2C3%2Ax%5E2%2B-4%2Ax%2B1%29+

and we can see that the roots are x=1 and x=1%2F3. This verifies our answer