Solving a Simple Quadratic Problem: 3x^2 - 12x + 11 with the Quadratic Formula

  • Thread starter BuBbLeS01
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In summary, the conversation is about using the quadratic formula to solve for 3x^2 - 12x + 11. The original equation is reduced to 12 +/- (sqrt 12)/6, which can be further simplified to 6 +/- (sqrt 3)/3 using the distributive property. The steps for simplifying are shown, with a reminder to pay attention to grouping symbols. The final result is 6 +/- (sqrt 3)/3, solving the original equation.
  • #1
BuBbLeS01
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Homework Statement


I am trying to use the quadratic formula for 3x^2 - 12x +11 and I am getting...
12 +/- (sqrt 12)/6 which is supposed to reduce to 6 +/- (sqrt 3)/3 and I can't figure it out...it's very sad!
 
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  • #2
[tex]\sqrt{12} = \sqrt{4*3}= \sqrt{4}\sqrt{3} =2\sqrt{3}[/tex]
 
  • #3
The 2/2 cancels, involving the distributive property.

You did not use grouping symbols correctly in your message, but see the steps:

((2*2*3) +/- (2*2*3)^(.5))/(2*3)
=((2*2*3) +/- (2)*(3^(0.5)))/(2*3)
= 2*(2*3 +/- (3^(0.5)))/(2*3)
Notice the factor of 2 in numerator and factor of 2 in denominator; you need to write these steps longhand so you can see clearly; no typesetting system here on my end...
... simplifies quite well to
=(2*3 +/- (3^(0.5)))/3
=(6 +/- (3^(0.5))/3

Also watch my work carefully in case I make any grouping symbol error. I just caught a few that I corrected, but again check carefully.
 
  • #4
rock.freak667 said:
[tex]\sqrt{12} = \sqrt{4*3}= \sqrt{4}\sqrt{3} =2\sqrt{3}[/tex]
So you have (12 * 2 * sqrt 3) / 6 which simplifies to (6 * 1 * sqrt3) / 3 then to
(6 * sqrt 3) / 3
 

Related to Solving a Simple Quadratic Problem: 3x^2 - 12x + 11 with the Quadratic Formula

What is a simple quadratic problem?

A simple quadratic problem is a mathematical equation that involves a quadratic function, which is a polynomial equation of the second degree. Quadratic problems typically involve finding the value(s) of the variable(s) that make the equation true.

What is the standard form of a simple quadratic equation?

The standard form of a simple quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. This form allows for easy identification of the coefficients and the constant term.

How do you solve a simple quadratic problem?

To solve a simple quadratic problem, you can use methods such as factoring, completing the square, or the quadratic formula. These methods involve manipulating the equation to isolate the variable and find its value. Some problems may have multiple solutions, while others may have no real solutions.

What are the real-life applications of simple quadratic problems?

Simple quadratic problems have various real-life applications, such as in physics, engineering, economics, and statistics. For example, projectile motion can be modeled using quadratic equations, and quadratic regression can be used to analyze data in statistics.

What is the difference between a simple quadratic problem and a complex quadratic problem?

A simple quadratic problem involves a quadratic equation with only one variable, while a complex quadratic problem involves multiple variables. Complex quadratic problems can also involve higher degrees of the variable, such as cubic or quartic equations.

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