SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. x2 + 6x - 7 = 0 z2 + z + 1 = 0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine whether the following equations have a solution or not? Justify your answer. x2 + 6x - 7 = 0 z2 + z + 1 = 0       Log On


   

Question 149270: Determine whether the following equations have a solution or not? Justify your answer.
x2 + 6x - 7 = 0
z2 + z + 1 = 0

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Quickest way is to graph the equations to check for real solutions.
x%5E2%2B6x-7
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%2B6x-7%29+
This can be factored into,
x%5E2%2B6x-7=%28x%2B7%29%28x-1%29
x=1 and x=-7 are zeros as you can see.
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z2%2Bz%2B1=0
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C++x%5E2%2Bx%2B1%29+
Never crosses the x axis, therefore no real solutions, the solutions are complex.