System of equation with parameters

[prayzesaint]

Hi!

I am having trouble with the following problem:

Find x values (x1, x2) in this equation [math]2x^2-(2a-5)x+a-3=0[/math]For which parameter a value:
1. x1 is double of x2
2. x1 and x2 absolute values are the same
3. x1 and x2 values are each other's inverted numbers

I already have simplified the equation, if that is even what you are supposed to do.

Thanks!

 

[lev888]

Hi!

I am having trouble with the following problem:

Find x values (x1, x2) in this equation [math]2x^2-(2a-5)x+a-3=0[/math]For which parameter a value:
1. x1 is double of x2
2. x1 and x2 absolute values are the same
3. x1 and x2 values are each other's inverted numbers

I already have simplified the equation, if that is even what you are supposed to do.

Thanks!

This is a quadratic equation. Apply the quadratic formula. You'll get 2 root expressions with a. The additional conditions let you make an equation out those 2 expressions, which you can solve for a.

 

[Steven G]

Ax²+Bx+C = 0

A = 2
B= -(2a-5) or 5-2a
C = a-3.

Let the fun begin.

 

[prayzesaint]

Thank you for your replies! They helped a lot.