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

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Homework Help Overview

The discussion revolves around determining the range of values for A in the quadratic equation Ay² - 3y + 4 = 0 that would result in both roots being real. Participants are exploring the implications of the discriminant in relation to the quadratic formula.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the concept of the discriminant and its role in identifying the nature of the roots of the quadratic equation. There are attempts to express the roots in terms of A and to understand how the discriminant affects the number of real solutions.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the discriminant and its application. Some guidance has been offered regarding the need for the discriminant to be greater than zero for two real roots, but there is still confusion among participants about how to proceed with the problem.

Contextual Notes

Participants are working with the information provided in the problem statement and are trying to derive necessary conditions for A without additional numerical values or examples.

mwhowell
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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.
 
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Can you express the roots in terms of A? Do you know what the discriminant is for a quadratic equation?
 
what is a discriminant?
 
The discriminant is the quantity inside the square root in the quadratic formula. You know the quadratic formula, right?
 
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
 
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?
 
yea i know how to use the quadratic formula but i am still really confused
 
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.
 
Basically they are trying to say that the discriminant must be greater than or equal to zero; find A.
 
  • #10
symbolipoint said:
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:
mwhowell said:
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?
 
  • #11
Yes. I see. TWO ROOTS REAL. Otherwise only one root.
 

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