How Do A and B as Roots Verify the Properties of a Quadratic Equation?

[mathdad]

Let A and B be the roots of the quadratic equation

ax^2 + bx + c = 0. Verify each statement below.

1. A + B = -b/a

2. AB = c/a

I need help getting started for parts 1 and 2. I will do the math.

 

[topsquark]

Let A and B be the roots of the quadratic equation

ax^2 + bx + c = 0. Verify each statement below.

1. A + B = -b/a

2. AB = c/a

I need help getting started for parts 1 and 2. I will do the math.

You can do it by hand:
\(\displaystyle A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

\(\displaystyle B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Add them together and you get A + B = -b/a. And you can do the multiplication for the second part. If you run into troubles, of course feel free to post us.

-Dan

 

[mathdad]

You can do it by hand:
\(\displaystyle A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

\(\displaystyle B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Add them together and you get A + B = -b/a. And you can do the multiplication for the second part. If you run into troubles, of course feel free to post us.

-Dan

I get it. Thanks.

 

[HallsofIvy]

I think it is simpler just to compare $$a(x- A)(x- B)$$ with $$ax^2+ bx+ c$$. Multiply the first and compare coefficients.

 

[mathdad]

I think it is simpler just to compare $$a(x- A)(x- B)$$ with $$ax^2+ bx+ c$$. Multiply the first and compare coefficients.

The word WITH is covering your LaTex.

 

[I like Serena]

The word WITH is covering your LaTex.

For the record, on a mobile device the fonts are typically increased in size automatically.
However, the MathJax that we use to render our formulas doesn't know about this, meaning that inline latex isn't resized to match.
It's only on mobile devices that inline latex is a problem. On tablets or laptops this problem does not occur. Latex on separate lines does not have this problem either.

 

[mathdad]

For the record, on a mobile device the fonts are typically increased in size automatically.
However, the MathJax that we use to render our formulas doesn't know about this, meaning that inline latex isn't resized to match.
It's only on mobile devices that inline latex is a problem. On tablets or laptops this problem does not occur. Latex on separate lines does not have this problem either.

I do not have a laptop or computer.

 

[I like Serena]

I do not have a laptop or computer.

On my mobile device the problem is a bit less in landscape mode, meaning the inline latex formulas are at least usually more or less readable.

 

[mathdad]

On my mobile device the problem is a bit less in landscape mode, meaning the inline latex formulas are at least usually more or less readable.

Good for you. Let's get back to math.

 

[MarkFL]

Good for you. Let's get back to math.

In all fairness, and I don't mean to be antagonistic at all, you brought up the issue again that inline LaTeX is a problem on your device. It would be unreasonable to expect the community at large to suddenly change our posting styles, developed over many years, to suit mobile devices, when most of us posting help are using PCs.

I like Serena was just trying to help by giving you a suggestion to minimize the issue. I have found him to know what he's talking about, whenever he talks. :D

 

[mathdad]

I like everyone here. Let's get back to math.

 

[mathdad]

You can do it by hand:
\(\displaystyle A = \frac{-b + \sqrt{b^2 - 4ac}}{2a}\)

\(\displaystyle B = \frac{-b - \sqrt{b^2 - 4ac}}{2a}\)

Add them together and you get A + B = -b/a. And you can do the multiplication for the second part. If you run into troubles, of course feel free to post us.

-Dan

Question:

Can I use the values of A and B in your reply to this question to show as given below?

1. A^2 + B^2 = (b^2 - 2ac)/(a^2)

2. 1/A^2 + 1/B^2 = (b^2 - 2ac)/(c^2)