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I tried searching before posting this, but couldn't find anything. I have this parametric* equation :

$ x^2 + 54x + 5a^2 = 0 $

They are asking me to find the values of a for which the roots of the equation will be

$x_{1} = (1/5)x_{2}$

The things that I tried :

  1. $ x_{1} + (1/5)x_{2} = (1/5)(-b/a) $

  2. $x_{1} * (1/5)x_{2} = (1/5)(c/a)$

But I can't get to the right answer. If you don't feel like explaining just tell me what am I doing wrong.

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Your strategy of using the Vieta relations works quickly.

Let the roots be $r$ and $5r$.

Then the sum of the roots is $6r$. It is also $-54$, so $r=-9$.

The product of the roots is $5(-9)^2$. It is also $5a^2$. So $a^2=81$.

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  • $\begingroup$ It did not came to me to do r = actual_root so when i tried with the actual roots it was not equal to -9... i guess i did not think hard enough $\endgroup$ Commented Nov 22, 2015 at 7:51

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