# What is quadratic Diophantine equation?

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## What is quadratic Diophantine equation?

The quadratic diophantine equations are equations of the type: a x 2 + b x y + c y 2 = d where , , and are integers, and we ask the solutions and to be integers.

### Is Diophantine equation solvable?

For instance, we know that linear Diophantine equations are solvable.

#### Is Pi a Diophantine?

In short, a diophantine approximation is the approximation of a real number using rational numbers. Pi π is an irrational number, which means it is followed by an infinite quantity of decimal places, and therefore its true value cannot be represented in a fractional manner.

**How do you solve linear Diophantine equations with two variables?**

Linear Diophantine equation in two variables takes the form of ax+by=c, where x,y∈Z and a, b, c are integer constants. x and y are unknown variables. A Homogeneous Linear Diophantine equation (HLDE) is ax+by=0,x,y∈Z. Note that x=0 and y=0 is a solution, called the trivial solution for this equation.

**What is the purpose of Diophantine equation?**

The purpose of any Diophantine equation is to solve for all the unknowns in the problem. When Diophantus was dealing with 2 or more unknowns, he would try to write all the unknowns in terms of only one of them.

## How do you solve Diophantine equations with 2 variables?

### What is non linear Diophantine equation?

A non- linear Diophantine equation is every Diophantine equation which is not linear. For instance, the equation x 2 + 3 y 3 = 35 is a non-linear Diophantine equation. In fact, we can say that we are going to use some simple tricks that will help us in solving such equations. Example 1.

#### What is an indeterminate solution?

From Wikipedia, the free encyclopedia. In mathematics, particularly in algebra, an indeterminate system is a system of simultaneous equations (e.g., linear equations) which has more than one solution (sometimes infinitely many solutions).

**Do quadratic equations always have two real solutions?**

A quadratic equation has at most two solutions. If there is no real solution, there are two complex solutions. If there is only one solution, one says that it is a double root. So a quadratic equation has always two roots, if complex roots are considered, and if a double root is counted for two.

**Why can a quadratic equation have only one imaginary solution?**

A quadratic equation cannot have one imaginary solution because of the discriminant enclosed in a radical. The discriminant, √(b² – 4ac), determines the nature of the roots and it can only be either 2 real roots, 1 real solution or 2 imaginary roots.

## What are the steps to solve the quadratic function?

Now we can solve a Quadratic Equation in 5 steps: Step 1 Divide all terms by a (the coefficient of x 2). Step 2 Move the number term (c/a) to the right side of the equation. Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.

### Why is a quadratic eqaution is called quadratic?

The name Quadratic comes from “quad” meaning square , because the variable gets squared (like x2 ). The Standard Form of a Quadratic Equation looks like this: a, b and c are known values. a can’t be 0. ” x ” is the variable or unknown (we don’t know it yet).