How to find a quadratic equation given the solution??

Questions
1

We are working on quadratic equations.

How would I enter x=4/5,x=3,x=-3 and get the equation??

or a=sqrt10,a=-sqrt10n and get the equation?

or x=(-1+_1i)/2 and get the equation?

I’m stummped!! Wolfram has been a nightmare on getting simple algebra help. thank you for any help !

2

Just enter the equation:

(x-a)(x-b)

where a and b are the two roots. That, of course, is the quadratic equation with those roots

3

I’m sorry but i didn’t understand your answer. I have the solution I need the equation from the solution.

do you know how to enter where the plus is over the minus for “plus or minus”

so sorry but I may have not asked the question right.

Here is an example : a=sqrt10, a= - sqrt10 what is the solution to this ?

Thank you !!

4

If a quadratic equation has two roots --let’s call them x1 and x2–then the equation is proportional to

(x-x1)(x-x2)

In your example

x1 = Sqrt[10]

x2 = -Sqrt[10]

so the equaiton is

(x-Sqrt[10])(x+Sqrt[10])

you can expand this out to get the equivalent

x^2 - 10
5

Ok, when I enter the equation in wolfram I don’t get the right answer which is a^2-10=0 .

I also cant figure out how to enter x=-1(plus or minus)1i /2 do you know if it will calculate that?

I so appreciate your help David !

6

My mistake, I wrote Sqrt[2] rather than Sqrt[10] :wink:

So I should have written

(x-Sqrt[10])(x+Sqrt[10])

I just edited my original post to correct this…

I do not believe that there is a way to enter the plus/minus character into Wolfram|Alpha. But when, in algebra, one uses that character it is just a shorthand for writing both cases.

I also note that one would hope that Wolfram|Alpha would give the answer to the statement

quadratic equation with roots 3 and 9

and give

27 - 12 x + x^2

as the result. But apparently the Wolfram|Alpha parser does note recognize this. I sent in a suggestion that it should address this case.

7

It’s really sad how I have tried to use wolfram alpha and rarely get correct answers. I started using other sites and got the answers. I tried to come back for this type of equation but can’t find the help anywhere. Thank you again and have a great night.

Ambi J