SOLUTION: solve the equation by using the quadratic formula 3z^2-8z+2=0

Question 94385: solve the equation by using the quadratic formula
3z^2-8z+2=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 z:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=-8, and c=2

Negate -8 to get 8

Square -8 to get 64 (note: remember when you square -8, 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

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph (just replace z with x), we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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