Positive Root Solutions for Quadratic Equations with Variable Coefficients

[Sumedh]

[SOLVED]

Homework Statement

Let$$4x^2-4(α-2)xα-2=0 (α\epsilon R)$$
be a quadratic equation, then find the value of α for which both the roots are positive.

Homework Equations

The Attempt at a Solution

the conditions will be
1) Discriminant D≥0
by this condition i got α (-∞,2][3,∞)
2) f(0) greater than or equal to 0
by this we get α (2,∞)

3) now should i use -b/2a(point exactly between both roots)
and equate as -b/2a greater than 0if-3rd point is right then what will be the final answer
α (?,?)union(?,?)
please provide help

 

[PeterO]

Homework Statement

Let$$4x^2-4(α-2)xα-2=0 (α\epsilon R)$$
be a quadratic equation, then find the value of α for which both the roots are positive.

Homework Equations

The Attempt at a Solution

the conditions will be
1) Discriminant D≥0
by this condition i got α (-∞,2][3,∞)
2) f(0) greater than or equal to 0
by this we get α (2,∞)

3) now should i use -b/2a(point exactly between both roots)
and equate as -b/2a greater than 0


if-3rd point is right then what will be the final answer
α (?,?)union(?,?)
please provide help

Are you sure the equation has typed up correctly? hopefully there should be a + or - sign between the x and the alpha??

 

[Sumedh]

Thanks,
I have solved the problem
there is a + sign.