I only have 1 hour to get this question answered. Thank you in advance. I need a quadratic equation in the variable x given the solutions:

Question

I only have 1 hour to get this question answered. Thank you in advance. I need a quadratic equation in the variable x given the solutions:

-7 sqrt 7, and 7 sqrt 7
This needs to be in the standard form of ax^2+bx+c=0.
Can someone please help me with this???? I am so lost!!!!

Answer 1

For a quadratic equation with given zeroes z1 and z2, the equation is:

(x-z1)(x-z2)=0
In the given case, z1=-7√7 and z2=7√7.
Expand and simplify the resulting expression on the left-hand-side, and equate coefficients of powers x², x and constant term to get the values of a, b and c.

I gave you response to a similar question, except that I forgot the variable x, which should have read:
x² -5√5x -30 = 0

see:

http://www.jiskha.com/display.cgi?id=1289541351

Answer 2

I understand, although mathlab checked it wrong and gave me this problem. I SIMPOLY do not understand this when it comes to radicals. And furthermore mathlab has a habit of checking problems wrong when they are indeed right.I understand how to FOIL, I just do not know how to work the radicals, CAN YOU PLEASE HELP ME!!!! This is due in 1 hour. Thank you so much!!!

Answer 3

And you are paying for Mathlab?

Answer 4

Just follow MathMate instructions and set it as

(x - 7√7)(x+7√7) = 0
looks like the difference of squares pattern, so ...

x^2 - 343 = 0

then
a=1
b=0
c=-343

try that as input

Answer 5

Of course, I'm here to help! To find a quadratic equation with the given solutions, you can use the fact that the solutions of a quadratic equation can be obtained by equating it to zero and then factoring.

Let's start with the solutions you provided: -7√7 and 7√7. Since they are both solutions, the quadratic equation should have factors that produce these values when set equal to zero.

To begin, let's set up the equation using the factored form:
(x - (-7√7))(x - 7√7) = 0
Simplifying, this becomes:
(x + 7√7)(x - 7√7) = 0

Expanding this expression using the foil method, we get:
x^2 - (7√7)x + (7√7)x - (7√7)(-7√7) = 0

Simplifying further, we have:
x^2 - 49 * 7 = 0

Multiplying 49 and 7, the equation becomes:
x^2 - 343 = 0

Now, the quadratic equation is in standard form:
x^2 - 343 = 0

You can also rewrite it with the terms in descending order:
x^2 - 343 + 0 = 0

Therefore, the quadratic equation in standard form with the given solutions is:
x^2 - 343 = 0

I hope this helps! Let me know if you have any further questions.