p1 help please its an easy question for good mathmaticians Watch

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dreamer86
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well i have the answer to this, but i dont know how to get there myself so any help would be greatfully recieved. also there is rep, but i think i can only give out one point so not much of an incentive, just the feel good factor of helping someone out okay, il get to the question..

Prove that the condition for the equation px^2-5x+p=0 to have real roots is -5/2<p<5/2.



the < are actually ones that are equal to as well but i didnt know how to type them

thankyou good people
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Gaz031
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(Original post by dreamer86)
well i have the answer to this, but i dont know how to get there myself so any help would be greatfully recieved. also there is rep, but i think i can only give out one point so not much of an incentive, just the feel good factor of helping someone out okay, il get to the question..

Prove that the condition for the equation px^2-5x+p=0 to have real roots is -5/2<p<5/2.
For real roots b^2 - 4ac>=0, from the quadratic equation. Otherwise you take the root of a negative number to form a complex number.

That is (-5)^2 - 4(p)(p) >=0
25 - 4p^2 >= 0
Critical points at 4p^2 = 25, p^2 = 25/4, p = 5/2 or -5/2
Check each region on the number line to see if the inequality holds will show you that 5/2>p>-5/2 is the correct area.
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dreamer86
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thankyou very much
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