Quadratic equations: 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0

[Alfredo]

We have 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0
For wich values of a and b the two equations have the same solutions?
Solution:
a=4/9 b=-2/3

 

[Otis]

We have 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0
For wich values of a and b the two equations have the same solutions?
Solution:
a=4/9 b=-2/3

Are those your solutions and you want to know if they are correct?

I checked them; they are correct.

 

[stapel]

We have 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0
For which values of a and b the two equations have the same solutions?
Solution: a=4/9 b=-2/3

You plugged each quadratic into the Quadratic Formula. You obtained results in terms of "a" and "b". And... then what?

Please be complete. Thank you!

 

[ChandrikaP]

We have 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0
For wich values of a and b the two equations have the same solutions?
Solution:
a=4/9 b=-2/3

yes those are right values.
if u have multiple choice answer then you need to do hit n trial.
and you need to put each value in eqaution n see are those two have same solution.

 

[Deleted member 4993]

yes those are right values.
if u have multiple choice answer then you need to do hit n trial.
and you need to put each value in equation n see are those two have same solution.

No .... you do not need trial and error method here.

We have 2x^2-(a+b)x+2a-b=0 and x^2+(a-b-1)x+a-2b-1=0
For which values of a and b the two equations have the same solutions?
Solution:
a=4/9 b=-2/3

One way would be:

2x^2-(a+b)x+2a-b = 2*x^2 + 2*(a-b-1)x + 2 * (a-2b-1)

-(a+b)x+ 2a-b = 2*(a-b-1)x + 2 * (a-2b-1)

-(a+b)x - 2*(a-b-1)x = 2 * (a-2b-1) - 2a + b

x (-a - b - 2a + 2b + 2) = 2a - 4b - 2 - 2a + b

x (-3a + b + 2) = - 3b - 2

To have same graph (one of the ways to get same solutions):

- 3a + b + 2 = 0

and

3b + 2 = 0

Now you have two equations and two unknowns - solve it

To get "all the values" of 'a' & 'b' for which the solutions will be equal - you would have to equate the quadratic solutions.