SOLUTION: Evaluate the discriminant of each equation. How many real and imaginary solutions does it have. 1. 4x^2-4x+1=0 2. x^2-6x+7=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Evaluate the discriminant of each equation. How many real and imaginary solutions does it have. 1. 4x^2-4x+1=0 2. x^2-6x+7=0      Log On


   

Question 433393: Evaluate the discriminant of each equation. How many real and imaginary solutions does it have.
1. 4x^2-4x+1=0
2. x^2-6x+7=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
These are in the form +ax%5E2+%2B+bx+%2B+c+=+0+
The discriminant is b%5E2+-+4%2Aa%2Ac+
(1)
++4x%5E2+-+4x+%2B+1+=+0+
+b%5E2+-+4%2Aa%2Ac+=+%28-4%29%5E2+-+4%2A4%2A1+
+16+-+16+=+0+
When the discriminant is 0, there is one real solution
Which is +%28-b%29%2F2a++=+-%28-4%29+%2F+%282%2A4%29+
+x+=+1%2F2+
--------------
(2)
The discriminant is +%28-6%29%5E2+-+4%2A1%2A7+=+36+-+28+
+36+-+28+=+8+
There are 2 real solutions which are
+%28-%28-6%29+%2B+sqrt%288%29+%29+%2F+%282%2A1%29+
+x+=+3+%2B+sqrt%282%29+
and
+%28-%28-6%29+-+sqrt%288%29+%29+%2F+%282%2A1%29+
+x+=+3+-+sqrt%282%29+