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**Nature of Roots of a Quadratic Equation**

## What are Quadratic Equations?

A quadratic equation is an equation in the form ax^2+bx+c=0, where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic equation is a parabola.

### How are Quadratic equations different from Quadratic Polynomials?

Quadratic equations are different from quadratic polynomials in that quadratic equations have a variable in the second power, while quadratic polynomials do not. Quadratic equations can be solved using the quadratic formula, while quadratic polynomials cannot.

#### Methods used for finding roots of Quadratic Equations

There are a few methods that can be used to find the roots of quadratic equations. The first is the quadratic formula, which can be used to solve any quadratic equation. The second is the graphical method, which can be used to find the roots of a quadratic equation by graphing the equation and finding the points where the graph crosses the x-axis. The third is the numerical method, which can be used to find the roots of a quadratic equation by using a calculator or computer to approximate the roots of the equation.

**Also Read:** **Discriminant – Explanation, Formula and Relationship between Roots**

#### Graphical Representation of Quadratic Equation

The graphical representation of a quadratic equation is a graph that shows the solutions to the equation. The equation will have a line that represents the equation, and the solutions will be represented by points on the line.

### Type of Roots

There are three types of roots:

**Axial Roots:**These are the long roots that run along the length of the plant.**Radicular Roots:**These are the shorter, fleshier roots that grow out of the stem.**Fibrous Roots:**These are the thin, branching roots that grow from the radicular roots.

### Nature of Roots

The nature of roots is one of the most important aspects of plant biology. Roots are the organs of a plant that anchor it in the soil and absorb water and minerals from the soil. The root system of a plant is also responsible for the distribution of water and nutrients throughout the plant.

**There are two main types of roots:** Taproots and Fibrous roots.

- Taproots are large, single roots that grow deep into the soil.
- Fibrous roots are small, thin roots that spread out horizontally in the soil.

Most plants have a combination of both taproots and fibrous roots. The type of root system a plant has depends on the type of plant and the environment in which it grows.

For example, plants that grow in dry environments typically have a more developed taproot system, while plants that grow in moist environments typically have a more developed fibrous root system.

**Facts**

- The EU is the world’s largest economy with a GDP of $17.5 trillion.
- The EU has a population of over 500 million people.
- The EU has 28 member states.
- The EU’s main economic sectors are services (60%), industry (30%), and agriculture (10%).
- The EU is the world’s largest exporter of goods (€1.7 trillion in 2016) and the second-largest importer (€1.5 trillion in 2016).
- The EU is the world’s largest donor of development assistance (€86.6 billion in 2016).
- The EU is a major source of foreign investment and has been the world’s largest recipient of foreign direct investment since 2001.
- The EU has a high level of human development, with an HDI of 0.891 (2015).
- The EU is a founding member of the United Nations, the NATO alliance, and the WTO.