Question

the nature of the quadratic form 2x^2+3y^2+2z^2+2xy is​

Answer 1

Answer:

The nature of the quadratic form 2x^2+3y^2+2z^2+2xy is​ conical form.

Step-by-step explanation:

Step : 1 A unique nonlinear function with just second-order terms is the quadratic form (either the square of a variable or the product of two variables). Classification of the quadratic form, section 1.2 Q = x Ax: A quadratic form is described as follows:

Step : 2  Q 0 for all x and Q = 0 for some x = 0 in the negative semidefinite form. c: Q is greater than zero when x is equal to zero.

Q 0 for all x and Q = 0 for some x = 0 in the positive semidefinite case (d). e: indefinite: For some x, Q > 0 and for other x, Q 0.

Step : 3  An expression of the form Q(x) = xTAx, where A is a nxn symmetric matrix, can be used to calculate the value of a function Q defined on R n at a vector x in R n. The type of roots depends on the discriminator.

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Answer 2

Answer:

The graph of a quadratic equation is a parabola, and it can be used to calculate the area underneath the curve and find the extrema of the equation.

Step-by-step explanation:

From the above question,

They have given :

The quadratic form 2$x^{2}$ + 3$y^{2}$ + 2$z^{2}$ + 2xy is a general form of a quadratic equation, which is a polynomial equation of degree 2.

It is composed of three parts: a coefficient, a variable, and a constant.

The coefficient is the number in front of the variable, and it determines the shape of the graph of the quadratic equation.

The variable is the letter of the equation, and the constant is the number at the end.

In this particular equation, the coefficient for $x^{2}$ is 2, for $y^{2}$ is 3, and for z2 is 2. The coefficient for the xy term is 2.

The graph of this equation will be an ellipse, which is a closed curve with two foci. The equation can also be simplified to,

                        y = - (1/3) $x^{2}$ - 2$y^{2}$.

The nature of the quadratic form is mainly used to define the relationships between two variables and it is a very useful tool in calculus. It is also used in algebra to solve equations of higher degree, such as cubic and quartic equations.

The graph of a quadratic equation is a parabola, and it can be used to calculate the area underneath the curve and find the extrema of the equation. In addition, it can also be used to solve systems of equations and calculate the roots of a polynomial equation.

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