SOLUTION: Question: What can you say about the solutions of this nonlinear system? y=4x^2+4 y=2x^2-4 (a) the system has no solution (b) the system has two real solutions (c) the syst

Algebra ->  College  -> Linear Algebra -> SOLUTION: Question: What can you say about the solutions of this nonlinear system? y=4x^2+4 y=2x^2-4 (a) the system has no solution (b) the system has two real solutions (c) the syst      Log On


   

Question 30334: Question:
What can you say about the solutions of this nonlinear system?
y=4x^2+4
y=2x^2-4
(a) the system has no solution
(b) the system has two real solutions
(c) the system had two imaginary solutions
(d) the system has on solution of multiplicity 2.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+4x%5E2+%2B+4
y+=+2x%5E2+-+4
subtract the 2nd from the 1st
0+=+4%2AX%5E2+%2B+4+-+2%2Ax%5E2+%2B+4
2%2Ax%5E2+%2B+8+=+0
2%2A%28x%5E2+%2B+4%29+=+0
divide both sides by 2
x%5E2+%2B+4+=+0
x+=+0%2B-+sqrt%28-4%29%29+
x+=+%2B%28sqrt%284%29+%2A+sqrt%28-1%29%29
x+=+%2B2%2Ai
also
x+=+-%28sqrt%284%29+%2A+sqrt%28-1%29%29
x+=+-2%2Ai
so, the answer is (c), the system has 2 imaginary solutions