SOLUTION: Please help with the the equation {{{ x^2-4x+1=0 }}} I understand a= 1 b=-4 c=1 and using {{{ b^2-4ac }}} Why is the the discriminant: {{{ 4^2-4*1*1 = 12 }}} and not

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help with the the equation {{{ x^2-4x+1=0 }}} I understand a= 1 b=-4 c=1 and using {{{ b^2-4ac }}} Why is the the discriminant: {{{ 4^2-4*1*1 = 12 }}} and not       Log On


   

Question 106068: Please help with the the equation +x%5E2-4x%2B1=0+
I understand a= 1 b=-4 c=1
and using +b%5E2-4ac+
Why is the the discriminant: +4%5E2-4%2A1%2A1+=+12+
and not +-4%5E2-4%2A1%2A1+=+12+
Shouldnt +b%5E2+ equal -4 not 4
Thanks



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2-4%2Ax%2B1=0 ( notice a=1, b=-4, and c=1)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Plug in a=1, b=-4, and c=1




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A1%2A1+%29%29%2F%282%2A1%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B-4+%29%29%2F%282%2A1%29 Multiply -4%2A1%2A1 to get -4




x+=+%284+%2B-+sqrt%28+12+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+2%2Asqrt%283%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%284+%2B-+2%2Asqrt%283%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%284+%2B+2%2Asqrt%283%29%29%2F2 or x+=+%284+-+2%2Asqrt%283%29%29%2F2



Now break up the fraction



x=%2B4%2F2%2B2%2Asqrt%283%29%2F2 or x=%2B4%2F2-2%2Asqrt%283%29%2F2



Simplify



x=2%2Bsqrt%283%29 or x=2-sqrt%283%29



So the solutions are:

x=2%2Bsqrt%283%29 or x=2-sqrt%283%29