Quadratic Solution Simplification: Is My Work Correct?

In summary, a quadratic equation is a second degree polynomial equation in the form of ax^2 + bx + c = 0. Simplifying quadratic solutions is important for making them easier to work with and understand, as well as identifying key features such as the vertex and x-intercepts. This can be done using methods such as the quadratic formula, completing the square, or factoring. The quadratic formula, x = (-b±√(b^2-4ac))/2a, can be used to find the solutions of any quadratic equation. The key features of a quadratic equation are the vertex and x-intercepts, which can be identified by simplifying the equation in standard form, y = ax^2 + bx + c
  • #1
montoyas7940
364
21

Homework Statement



Simplify [tex]\frac{-2\pm\sqrt{-56}}{30}[/tex]

[tex]\frac{-2\pm 2i\sqrt{14}}{30}[/tex]

[tex]\frac{-1\pm i\sqrt{14}}{15}[/tex]

Is this correct?
 
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  • #2
Yes. I would write it with =, though.
[tex]\frac{-2\pm\sqrt{-56}}{30}~=~\frac{-2\pm 2i\sqrt{14}}{30}~=~\frac{-1\pm i\sqrt{14}}{15}[/tex]
 
  • #3
Thank you, I am very rusty...
 
  • #4
montoyas7940 said:
Thank you, I am very rusty...
Well, it doesn't show. There was no problem with your work. I was just polishing it a bit.
 

FAQ: Quadratic Solution Simplification: Is My Work Correct?

What is a quadratic equation?

A quadratic equation is a mathematical equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. It is also known as a second degree polynomial equation.

Why do we need to simplify quadratic solutions?

Simplifying quadratic solutions makes them easier to work with and understand. It also helps to identify key features of the equation, such as the vertex and x-intercepts.

How do we simplify quadratic solutions?

To simplify quadratic solutions, we can use the quadratic formula, completing the square, or factoring. These methods can help us to rewrite the equation in a simpler form.

What is the quadratic formula?

The quadratic formula is a formula used to solve quadratic equations of the form ax^2 + bx + c = 0. It is written as x = (-b±√(b^2-4ac))/2a and can be used to find the solutions (roots) of any quadratic equation.

What are the key features of a quadratic equation?

The key features of a quadratic equation are the vertex, which is the highest or lowest point on the parabola, and the x-intercepts, which are the points where the parabola crosses the x-axis. These features can be identified by simplifying the quadratic solution in standard form, y = ax^2 + bx + c.

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