Quadratic inequalities for complex variables?by mathsciguy Tags: complex, inequalities, quadratic, variables 

#1
Sep1213, 09:29 AM

P: 132

Hello, I was looking at Riley's solution manual for this specific problem. Along the way, he ended up with a quadratic inequality:
how.bmp If you looked at the image, he said it is given that λ is real, but he asserted that λ has no real roots because of the inequality. Doesn't that mean λ is imaginary or complex in some points then, contradicting his first statement? I reckon this has something to do with the properties of a quadratic inequality for complex variables. 



#2
Sep1213, 10:59 AM

HW Helper
P: 775





#3
Sep1313, 05:06 AM

P: 132

That's cool, I get it now. Then that means the roots are either purely imaginary or complex (but not purely real) right? Then why is it required that the discriminant be less than zero? Is it because it will make sure that part of the solution will have an imaginary part?




#4
Sep1313, 09:11 AM

HW Helper
P: 775

Quadratic inequalities for complex variables? 


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