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Quadratic

Posted June 3rd, 2009 by alpha
in

If every pair from among the equations $ x^2+px+qr=0 $ , $ x^2+qx+rp=0 $and $ x^2+rx+pq=0 $ has a common root, then the product of three common root is
a)pqr b)2pqr c)$ p^2q^2r^2 $ d)none of these

‹ Hi I'm new here and just wanted to say thanks Quadratic ›

Comments

answer

On June 3rd, 2009 Structure says:
$$x_1x_2=pq$$
$$x_2x_3=qr$$
$$x_3x_1=rp$$
$$x_1^2x_2^2x_3^2=p^2q^2r^2$$

From the first two equations we have

$$x(p-q)=r(p-q)$$

so as we suppose $<br /> p\neqq $

$$x_3=r$$

so

$$x_1x_2x_3=pqr$$

~~THANK YOU ~~

On June 6th, 2009 alpha says:

````Maths````
000
(((())))
///

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