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If one root of ax^{2}+2bx+c= 0 is double the other root. Then 

Option: 1

9b^{2}= 8ac


Option: 2

8b^{2}= 9ac


Option: 3

8a^{2}= 9bc


Option: 4

8c^{2}= 9ab


Answers (1)

best_answer

Let \alpha & 2\alpha be the roots of equation

Using sum of roots formula on given equation

\therefore \alpha +2\alpha =\frac{-2b}{a}\: \Rightarrow \: 3\alpha =\frac{-2b}{a}\: \Rightarrow \: \alpha =\frac{-2b}{3a}

\because \: \alpha is root of quadratic , So it will satisfy the equation.

a\left ( \frac{4b^{2}}{9a^{2}} \right )-\frac{4b^{2}}{3a}+c=0

\Rightarrow \: c=\frac{4b^{2}}{3a}-\frac{4b^{2}}{9a}\: \Rightarrow \: c=\frac{8b^{2}}{9a}

\Rightarrow \: 8b^{2}=9ac

\therefore Option (B)

Posted by

Irshad Anwar

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