quadratic Equation

Posted May 21st, 2009 by alpha

Ratio of roots of equation $(a+1)x^2-5x+3=0$ is (3/a)-1 , than find the value of 25 $a^2$ -48a

Comments

On May 21st, 2009 alpha says:

a)27 b)-27 c)108 d)None of these

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On May 21st, 2009 alpha says:

$\frac{\alpha}{\beta}=\frac{3}{a}-1$
$\frac{\alpha}{\beta}=\frac{3-a}{a}$

$\frac{\alpha+\beta}{\alpha-\beta}=\frac{3-a+a}{3-a-a}$ [Componendo & Dividendo]

Am I doing it correctly?

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On May 22nd, 2009 alpha says:

Please reply soon.

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On May 22nd, 2009 Structure says:

Correct answer is -27.

$x_1+x_2=\frac{5}{a+1}$

$x_1x_2=\frac{3}{a+1}$

$\frac{x_1}{x_2}=\frac{3}{a}-1$

$\frac{x_1}{x_2}+1=\frac{3}{a}$

$\frac{x_1+x_2}{x_2}=\frac{3}{a}$

$\frac{x_2}{x_1+x_2}=\frac{a}{3}$

$x_2=\frac{5a}{3(a+1)}$

$x_1=\frac{9}{5a}$

$x_1+x_2=\frac{9}{5a}+\frac{5a}{3(a+1)}=\frac{5}{a+1}$

$25a^2+27a+27-75a=0$

$25a^2-48a+27=0$