Range of values in regards to quadratics and discriminant

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To determine the range of values for the constant a in the inequality ax^2 + 2ax + 3 ≥ 0, the discriminant must be analyzed. The correct discriminant is 4a^2 - 12a, which should be non-positive for the quadratic to have all real solutions. Setting the discriminant to zero gives critical points, leading to the conclusion that the range of a is 0 < a ≤ 3. This ensures that the quadratic does not cross the x-axis, maintaining non-negativity. Understanding the relationship between the discriminant and the quadratic's behavior is crucial for solving the problem.
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Homework Statement



Determine the range of values of the constant a so that the solution of ax^2+2ax+3>=0 (when a >0) is all real numbers



Homework Equations



D = b^2-4ac


The Attempt at a Solution



The discriminant is 0, 3. I need to know how to arrange them to get the range. The range is 0<a<=3 in the answers. How do I get it?
 
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ybhathena said:

Homework Statement



Determine the range of values of the constant a so that the solution of ax^2+2ax+3>=0 (when a >0) is all real numbers



Homework Equations



D = b^2-4ac


The Attempt at a Solution



The discriminant is 0, 3.
No, the discriminant is 4a2 - 12a. What do your two values have to do with the discriminant? (I know, but I am trying to get you to be accurate in what you say.)
ybhathena said:
I need to know how to arrange them to get the range. The range is 0<a<=3 in the answers. How do I get it?
 

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