SOLUTION: True or false The equation x^ + x + 1 = 0 has two real roots and sqrt3 is an irrational number

Algebra ->  Geometry-proofs -> SOLUTION: True or false The equation x^ + x + 1 = 0 has two real roots and sqrt3 is an irrational number       Log On


   

Question 1053167: True or false
The equation x^ + x + 1 = 0 has two real roots and sqrt3 is an irrational number
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
No. Not this:
x^ + x + 1 = 0


You want this:
x^2 + x + 1 = 0
which means
x%5E2+%2B+x+%2B+1+=+0

Factorable? No.
General solution for a quadratic equation makes solutions
x=%28-1%2B-+sqrt%281%5E2-4%2A1%2A1%29%29%2F2
but upon simplification
x=%28-1%2B-+sqrt%28-3%29%29%2F2 WHICH ARE NOT REAL.

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
sqrt%283%29 is irrational number.

It is TRUE.

See the lesson
    - Proving irrationality of some real numbers
in this site.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

True or false
The equation x^ + x + 1 = 0 has two real roots and sqrt3 is an irrational number
x%5E%28what%29?