SOLUTION: why is x2 + 3x + 1 non-factorable?

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: why is x2 + 3x + 1 non-factorable?       Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 268678: why is x2 + 3x + 1 non-factorable?

Answer by josmiceli(9686) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+3x+%2B+1
I can try to factor it with quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
where
a+=+1
b+=+3
c+=+1
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+
x+=+%28-3+%2B-+sqrt%28+9+-+4+%29%29%2F2+
x+=+%28-3+%2B-+sqrt%285%29%29%2F2+
solutions are:
x+=+%28-3+%2B+sqrt%285%29%29%2F2
and
x+=+%28-3+-+sqrt%285%29%29%2F2
If the factors are x+-+a and x+-+b
where a and b are the roots,
x+-+%28-3+-+sqrt%285%29%29%2F2 and
x+-+%28-3+%2B+sqrt%285%29%29%2F2
are the factors of the equation