SOLUTION: What is the root of X^2+X+1=0? I have no idea how to do roots. Thanks again!

Question 92972: What is the root of X^2+X+1=0?
I have no idea how to do roots. Thanks again!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's use the quadratic formula to find the roots:

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=1

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

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

RELATED QUESTIONS
I have absolutely no idea how to start because I don't really understand what the... (answered by SAT Math Tutor)

Solve the following equation. |0 0 -1| |3 x 0 | = x^2 |2 0 3 | Please help! I have... (answered by MathLover1)

I have no idea why function problems scare me! Here's my questions: Find the domain for (answered by stanbon)

1. What is the determinant of the matrix [-1 2][1 3]. The [1 3] is directly under the [-1 (answered by venugopalramana)

How is x-5 a factor of the polynomial x^2-x-20? I know that x-5 is the answer but I have (answered by robertb)

Use the discriminant to determine how many real-number roots the equation has. Do not... (answered by Earlsdon)

simplify -x^2y^2/x^1/2y^0 i have no idea how to do this. help... (answered by texttutoring)

What is 1-2+3-4+5-6+...+2013? I have no idea how to do this problem. The answer is... (answered by Alan3354,ikleyn)

(6x-5)^2/3 = x^1/3 I have no idea what to... (answered by stanbon,tutor_paul)