Solve Quadratic Equation: 3x²+12x+c=0

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Discussion Overview

The discussion revolves around solving the quadratic equation 3x² + 12x + c = 0, specifically exploring the values of c that yield different types of solutions: one real solution, two real solutions, and two nonreal (complex) solutions. The scope includes mathematical reasoning and application of the quadratic formula.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant expresses difficulty in solving the quadratic equation and seeks assistance in determining the values of c for different solution types.
  • Another participant introduces the quadratic formula and prompts a discussion on the condition for having only one solution.
  • A subsequent post reiterates the condition for one solution, suggesting it relates to when a specific expression equals zero.
  • A participant clarifies that the discriminant D = 12² - 4(3)c is relevant to the discussion and questions what equals zero in this context, encouraging others to solve for c.

Areas of Agreement / Disagreement

Participants are engaged in a collaborative exploration of the problem, but there is no consensus yet on the specific values of c or the conditions for the different types of solutions.

Contextual Notes

The discussion relies on the understanding of the discriminant and its implications for the nature of the roots of the quadratic equation, but specific assumptions or definitions may not be fully articulated.

PhantomTechnic
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Hello I've been stuck on this test review question for a few days, and I can't figure it out. Can someone help out?
"3x²+12x+c=0, Find solutions for c, where there is 1 real solution, 2 real solutions, and 2 nonreal(complex) solutions"
 
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Hello and welcome to MHB, PhantomTechnic! (Wave)

Let's review the quadratic formula:

Given the quadratic equation:

$$ax^2+bx+c=0$$

Then the solution is given by:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Now, looking at that formula, what condition do we need for there to be only 1 solution?
 
MarkFL said:
Hello and welcome to MHB, PhantomTechnic! (Wave)

Let's review the quadratic formula:

Given the quadratic equation:

$$ax^2+bx+c=0$$

Then the solution is given by:

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Now, looking at that formula, what condition do we need for there to be only 1 solution?
Wouldn't it be when it equals zero?
 
PhantomTechnic said:
Wouldn't it be when it equals zero?

When what equals zero? You are headed in the right direction, but I want to make certain you are talking about the correct expression...D
 
To answer Mark, D = 12² - 4(3)c, where D is the discriminant. What equals 0?
Solve for c. What do you get? It's probably not a prime number!
 

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