what is the use of quadratic form .?

Question

for ex this equation is in quadratic form
ax(squar)+by(squar)+2xy

Answer 1

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example, the distance between two points in three-dimensional Euclidean space is found by taking the square root of a quadratic form involving six variables, the three coordinates of each of the two points.

Quadratic forms in one, two, and three variables are given by:

F(x) = ax2
F(x,y) = ax2 + by2 + cxy
F(x,y,z) = ax2 + by2 + cz2 + dxy + exz + fyz
Note that general quadratic functions and quadratic equations are not examples of quadratic forms.

Answer 2

question form a million : For this equation ( x ) * ( x - 11 ) = -24 , answer here questions : A. Use factorization to discover the muse of the equation ! answer form a million : First, we could desire to turn this equation ( x ) * ( x - 11 ) + 24 = 0 right into a*x^2+b*x+c=0 kind. ( x ) * ( x - 11 ) + 24 = 0 , amplify the left hand ingredient. <=> x^2 - 11*x + 24 = 0 <=> x^2 - 11*x + 24 = 0 The equation x^2 - 11*x + 24 = 0 is already in a*x^2+b*x+c=0 kind. because of the fact the fee is already arranged in a*x^2+b*x+c=0 kind, we get the fee of a = a million, b = -11, c = 24. 1A. Use factorization to discover the muse of the equation ! x^2 - 11*x + 24 = 0 ( x - 8 ) * ( x - 3 ) = 0 So we've the solutions x1 = 8 and x2 = 3

Answer 3

ax^2 + by^2 +2xy (say) = c
where a,b,c are constants and x,y variables.

You have two variables and one eqaution.
the basic rule of mathematics is that, you should have an amount of equations that matches the number of variables.

the use of quadratic form is that even if you have only one variable and a quadratic equation, there is a solution for the variable. the variable may have 2 solutions maximum.

similarly, if you have had two quadratic equations for the two variables, you could have got solutions for both the variables to a maximum no of 2 each, providing a set of four solutions.

Answer 4

For the discriminant form like solving b2-4ac (square root) then you just plug it in from -b + or - the delta ^ which was b2-4ac square root over 2a. There's one for completing the square x2+x+c=0

Answer 5

There is only one benefit as far as I can tell: it is used to calculate trajectories of artillary shells. I used to think it was useless, then someone told me it was useful for that.
The one thing to remember is if you can do a quadratic you can balance a check book, which is far more important.

Answer 6

it helps you to find the value of 2 unknown values (x and y in this case). The example you have given allows you to put the equation into 2 brackets to resolve the quantities.

Answer 7

to find the roots of the equation, if the roots are not real

in the equation u gave
x = [-b +/- root(b^2 - 4ac)] / 2a

Answer 8

To get the value and to do some advanced factor.

Answer 9

TO CORRUPT THE MINDS OF US YOUNG PEOPLE TO SO CALL USE IT IN THE FUTURE SAID BY MATH TEACHERS

Answer 10

i dont have a clue