Math Is Fun Forum

Annoying Bumpkin

Guest

Help: Understanding Quadratic Equation Roots Property

Hi;

I need help with understanding the following properties of the roots of a quadratic equation.

In my workbook it says:

Sum of Roots =

Products of Roots =

There's no explanation for why, my teacher didn't explain it either. I want to know!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help: Understanding Quadratic Equation Roots Property

Hi;

I fixed your latex.

This will help.

http://www.mathsisfun.com/algebra/polyn … roots.html

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help: Understanding Quadratic Equation Roots Property

Or, refer to my method!

Let s and t be solutions to the Quadratic

From the Quadratic Equation, we can split the ± sign so that each corresponds to s or t. In other words,

and

.

Adding them together gives

. The Square Roots cancel out to get

and simplifying gives

.

Similarly, multiplying them will get you

Last edited by evene (2016-02-14 04:59:11)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Help: Understanding Quadratic Equation Roots Property

Hej, evene

That is indeed correct, but I feel the approach given on MIF might be a bit more satisfying, as stating that the roots of a quadratic equation are this and that just makes you wonder about how we got that formula, which in turn brings you to a variation of the explanation over there.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

evene

Member

Registered: 2015-10-18

Posts: 272

Re: Help: Understanding Quadratic Equation Roots Property

Hej, anonimnystefy

I guess...

There's such thing as a Realmember?!? Wow... You guys sure spent a lot of time designing the website.

Last edited by evene (2016-02-14 06:38:13)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help: Understanding Quadratic Equation Roots Property

MIF is the designer.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.