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

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 Question 160425: How to show that the equation x^2 + px -q^2 = 0 are real for any real numbers p & q? ThanksAnswer by jim_thompson5910(29613)   (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"