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

In summary, the problem is asking for the range of possible values for A such that the equation Ay2 - 3y + 4 = 0 has two real roots. This can be determined by examining the discriminant, which is the quantity inside the square root in the quadratic formula. If the discriminant is greater than 0, there are two real solutions. If it is equal to 0, there is one real solution. And if it is less than 0, there are no real solutions. Therefore, the range of possible values for A is any value greater than 0.
  • #1
mwhowell
17
0

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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  • #2
Can you express the roots in terms of A? Do you know what the discriminant is for a quadratic equation?
 
  • #3
what is a discriminant?
 
  • #4
The discriminant is the quantity inside the square root in the quadratic formula. You know the quadratic formula, right?
 
  • #5
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
 
  • #6
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?
 
  • #7
yea i know how to use the quadratic forumla but i am still really confused
 
  • #8
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.
 
  • #9
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.
 

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

What is the range of values for A that will result in real roots for the equation Ay2 - 3y + 4 = 0?

The range of values for A is any real number except for 0. If A = 0, the equation becomes 0y2 - 3y + 4 = 0, which does not have real roots.

Is there a specific value of A that will result in only one real root for the equation Ay2 - 3y + 4 = 0?

Yes, if A = 1, the equation becomes y2 - 3y + 4 = 0, which has only one real root at y = 2.

Can the value of A be negative for the equation Ay2 - 3y + 4 = 0 to have real roots?

Yes, the value of A can be negative. In fact, any negative value of A will result in two real roots for the equation.

How many real roots does the equation Ay2 - 3y + 4 = 0 have if A is a rational number?

If A is a rational number, the equation will have two real roots. This is because a rational number can be written as a fraction, and when the fraction is squared, it will always result in a positive value.

Is there a limit to the range of values for A that will result in real roots for the equation Ay2 - 3y + 4 = 0?

No, there is no limit to the range of values for A. As long as A is a non-zero real number, the equation will have real roots.

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