SOLUTION: How to show that the equation x^2 + px -q^2 = 0 are real for any real numbers p & q? Thanks

Question 160427: How to show that the equation x^2 + px -q^2 = 0 are real for any real numbers p & q? Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Multiply

So for any value of "p", the value of is nonnegative. So is always nonnegative (ie it is zero or a positive number).

Also for any value of "q", the value of is nonnegative. So by extension, is always nonnegative.

So this means that is always nonnegative which means that and . Since the discriminant D is greater than or equal to zero, this means that the equation will have real solutions for any values of "p" and "q"
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