Solving for a & b: Increasing GP Equations

[utkarshakash]

Homework Statement

If $x_1,x_2$ are the roots of $x^2-3x+a=0$ and $x_3,x_4$ are the roots of the equation $x^2-12x+b=0$ and $x_1,x_2,x_3,x_4$ are in increasing G.P., find a and b

Homework Equations

The Attempt at a Solution

$x_1+x_2=3 \\<br /> x_1x_2=a \\<br /> x_3+x_4=12 \\<br /> x_3x_4=b$

But these are not sufficient to find a and b. Also what is meant by an increasing G.P.?

 

[SammyS]

Homework Statement

If $x_1,x_2$ are the roots of $x^2-3x+a=0$ and $x_3,x_4$ are the roots of the equation $x^2-12x+b=0$ and $x_1,x_2,x_3,x_4$ are in increasing G.P., find a and b

Homework Equations

The Attempt at a Solution

$x_1+x_2=3 \\<br /> x_1x_2=a \\<br /> x_3+x_4=12 \\<br /> x_3x_4=b$

But these are not sufficient to find a and b. Also what is meant by an increasing G.P.?

G.P. = Geometric Progression

http://en.wikipedia.org/wiki/Geometric_progression

 

[Saitama]

But these are not sufficient to find a and b. Also what is meant by an increasing G.P.?

It means that the common ratio of the GP is greater than 1.

 

[utkarshakash]

It means that the common ratio of the GP is greater than 1.

This means that $x_1<x_2<x_3<x_4$
But what is the use of this in my question?

 

[Mentallic]

This means that $x_1<x_2<x_3<x_4$
But what is the use of this in my question?

Ignoring that detail for the moment, simply try answer the question and then you'll see.