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&lt;x_2&lt;x_3&lt;x_4
But what is the use of this in my question?

 

[Mentallic]

This means that x_1&lt;x_2&lt;x_3&lt;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.