SOLUTION: By completing the square, or otherwise, prove that the inequality x^2 - 2px + q > 0 holds for all values of x if an only if q > p^2. Find the range of values of x in terms of p

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Question 974021: By completing the square, or otherwise, prove that the inequality x^2 - 2px + q > 0 holds for all values of x if an only if q > p^2.
Find the range of values of x in terms of p for which the inequality is broken if q = p^2 - 1
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant must be negative.
%28-2p%29%5E2-4%2Aq%3C0
4p%5E2-4q%3C0
p%5E2-q%3C0
p%5E2%3Cq
q%3Ep%5E2

That may or may not be too helpful for your second question, and you might want to ask that again in another help posting request. Before doing that, try solving x%5E2-px%2Bp%5E2-1%3E0 and see what you find. (General solution for a quadratic equation).