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What is the relationship between the solutions to a quadratic equation and why does it vary?
If you have a quadratic equation of the form
x^2 + bx + c = 0 and its solutions are x = p and x = q
then the relations between the solutions are:
- p + q = -b, and
- pq = c
These relations do not vary.
What else can I help you with?
What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
What is the difference between quadratic equation and quadratic expression?
an equation has an equals sign.
The difference between Quadratic function and quadratic equation?
dunctions are not set equal to a value
How is it possible for one equation to have many solutions?
An equation can have many solutions because it often represents a relationship between variables that can be satisfied by multiple sets of values. For instance, linear equations in two variables describe a line on a graph, where every point on that line is a solution. Similarly, quadratic equations can yield multiple solutions due to their parabolic shape, where different x-values can yield the same y-value. Thus, the nature of the equation and its graphical representation can lead to a multitude of solutions.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
What are the pros and cons of the quadratic equation?
Pros: There are many real life situations in which the relationship between two variables is quadratic rather than linear. So to solve these situations quadratic equations are necessary. There is a simple equation to solve any quadratic equation. Cons: Pupils who are still studying basic mathematics will not be told how to solve quadratic equations in some circumstances - when the solutions lie in the Complex field.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What is the difference between quadratic equation and quadratic expression?
an equation has an equals sign.
What is the difference between and linear relationship and a quadratic relationship?
a linear relationship is characterized by the form y=mx+b and a quadratic relationship is characterized by the form y=x^2+bx+c. Graphically represented, a linear equation forms a line and a quadratic will appear as a parabola.
The difference between Quadratic function and quadratic equation?
dunctions are not set equal to a value
How is it possible for one equation to have many solutions?
An equation can have many solutions because it often represents a relationship between variables that can be satisfied by multiple sets of values. For instance, linear equations in two variables describe a line on a graph, where every point on that line is a solution. Similarly, quadratic equations can yield multiple solutions due to their parabolic shape, where different x-values can yield the same y-value. Thus, the nature of the equation and its graphical representation can lead to a multitude of solutions.
What is the relationship between x and y in mathematics?
In mathematics, the relationship between x and y is often represented by an equation or a function. This relationship shows how the value of y changes based on the value of x. It can be linear, quadratic, exponential, or any other type of relationship depending on the specific equation or function being used.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
What is the difference between linear and quadratic equations?
A linear equation has the form of mx + b, while a quadratic equation's form is ax2+bx+c. Also, a linear equation's graph forms a line, while a quadratic equation's graph forms a parabola.
What is general equation?
A general equation typically refers to a mathematical expression that represents a relationship between variables. It can take various forms depending on the context, such as linear equations, quadratic equations, or differential equations. The general equation aims to encapsulate a wide range of specific cases or instances within its framework, often allowing for the derivation of particular solutions by substituting specific values for the variables.
What is an equation that has the variables x and y called?
An equation that involves the variables x and y is typically called a bivariate equation. It represents a relationship between the two variables and can often be graphed as a curve or line on a coordinate plane. Common forms include linear equations, quadratic equations, and others depending on the relationship defined by the equation.
