SOLUTION: Apply the quadratic formula to find the roots of the given function, and then graph the function. g(x) = x2 + x + 12

Question 144838: Apply the quadratic formula to find the roots of the given function, and then graph the function.
g(x) = x2 + x + 12
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=1, and c=12

Square 1 to get 1

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 1 to get 2

So the roots are

or

Notice if we graph the quadratic , we get

graph of

We can see that there are no real roots

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