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Help with math extension 2 question, thanks! (1 Viewer)

creativemaster

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Let H and K be the points representing the roots of
x^2 +2px+q=0, where p and q are real and p^2 <q . Find the algebraic relation satisfied by p and q in each of the following cases
(i) angle HOK is a right angle.
(ii) A, B, H and K are equidistant from the origin.
 

fan96

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This question should go in the Maths subforum.



Because , we can use the identity with and .

(Note that this identity is not valid if both and are negative)

Hence,



Where and are both real numbers.

Therefore, the gradient of the line joining the root to the origin in the complex plane is given by



And recall that the requirement for two lines to be perpendicular is that their gradients multiply to be .

The rest should be easy.
 

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