Eventually. E.g. http://www.wolframalpha.com/input/?i=x^2+5y^2-3z^2=7 and https://en.wikipedia.org/wiki/QuadricLeo Authersh said:If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?
No.Leo Authersh said:If a quadratic equation of two variables represents a conic section (planar intersection of a cone), then does a quadratic equation of three variables represent the complete cone?
A quadratic equation with three variables is a polynomial equation that contains three variables, typically represented as x, y, and z. It is expressed in the form of ax2 + bx + cy + d = 0, where a, b, and c are constants and x, y, and z are variables.
A quadratic equation with three variables can be solved using various methods such as substitution, elimination, or graphical methods. The most common method is the substitution method, where one variable is solved in terms of the other and substituted into the equation to solve for the remaining variable.
A quadratic equation with three variables can have either one or two real solutions, depending on the values of the variables and constants. If the discriminant (b2 - 4ac) is positive, then the equation will have two real solutions. If the discriminant is zero, the equation will have one real solution. If the discriminant is negative, the equation will have no real solutions.
Yes, a quadratic equation with three variables can have complex solutions. If the discriminant is negative, the equation will have two complex solutions in the form of a + bi, where a and b are real numbers and i is the imaginary unit.
Quadratic equations with three variables are used in various fields such as physics, engineering, and economics to model and solve real-life problems. For example, they can be used to calculate the maximum or minimum value of a function, determine the trajectory of a projectile, or analyze the cost and revenue of a business.