Find-the-relation-between-p-q-and-r-if-one-of-the-root-of-the-equation-px-2-qx-r-0-is-double-the-other-

Question Number 52573 by Necxx last updated on 09/Jan/19

F i n d t h e r e l a t i o n b e t w e e n p q a n d r

i f o n e o f t h e r o o t o f t h e e q u a t i o n

{p x}^{2} + q x + r = 0 i s d o u b l e t h e o t h e r .

Answered by mr W last updated on 09/Jan/19

{p x}^{2} + q x + r = p (x - a) (x - 2 a)

{p x}^{2} + q x + r = p (x^{2} - 3 a x + 2 a^{2})

\Rightarrow q = - 3 p a

\Rightarrow r = 2 {p a}^{2}

\Rightarrow r = 2 p {(- \frac{q}{3 p})}^{2} = \frac{2 q^{2}}{9 p}

\Rightarrow 9 p r = 2 q^{2}

Commented by Necxx last updated on 10/Jan/19

t h a n k y o u s i r

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