SOLUTION: Solve by using quadratic formula 4x^2-3x+3=0

Question 113718This question is from textbook Beginning Algebra
: Solve by using quadratic formula
4x^2-3x+3=0 This question is from textbook Beginning Algebra

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=4, b=-3, and c=3

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, 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 4 to get 8

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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