Range of A for Real Roots of Ay2 - 3y + 4 = 0

[mwhowell]

Homework Statement

Consider the following equation in y: Ay2 – 3y + 4 = 0.

What is the range of possible values for A such that the two roots are both real?

Homework Equations

The Attempt at a Solution

Not sure how to approach this problem.

 

[fzero]

Can you express the roots in terms of A? Do you know what the discriminant is for a quadratic equation?

 

[mwhowell]

what is a discriminant?

 

[Mark44]

The discriminant is the quantity inside the square root in the quadratic formula. You know the quadratic formula, right?

 

[mwhowell]

yea i know the quadratic formula but we are not given the value inside the square root. all the info we are given is stated in the problem up there

 

[Mark44]

The value of the discriminant tells you how many real solutions there are.

If the discriminant > 0, there are two real solutions.
If the discriminant = 0, there is one real solution.
If the discriminant < 0, there are no real solutions (there are two complex solutions).

Do you know how to use the quadratic formula?

 

[mwhowell]

yea i know how to use the quadratic formula but i am still really confused

 

[fzero]

Well as a first step, can you use the quadratic formula to determine an expression for the roots of A y² – 3y + 4 = 0? Once you do that, you might want to carefully examine the quantity in the square root.

 

[symbolipoint]

Basically they are trying to say that the discriminant must be greater than or equal to zero; find A.

 

[eumyang]

Basically they are trying to say that the discriminant must be greater than or equal to zero; find A.

Not greater than or equal to zero; just greater than. The original problem:

Consider the following equation in y: Ay2 – 3y + 4 = 0.

What is the range of possible values for A such that the two roots are both real?

 

[symbolipoint]

Yes. I see. TWO ROOTS REAL. Otherwise only one root.