## What is the main purpose of the quadratic formula?

The quadratic formula provides the roots (also called zeroes or x-intercepts) of a quadratic equation. A quadratic equation is a second-degree equation; its highest term is raised to the second power. Quadratic equations take the form of a parabola.

### What is the quadratic formula used for in real life?

In real life, the quadratic formula helps us in determining the area of space, the speed of a moving object, the value of profit gained on a product, and more. Even the path of a space rocket is described in terms of a quadratic equation.

**What are the 4 natures of quadratic equation?**

The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

**Why was the quadratic formula invented?**

It is known that the Egyptian wisemen (engineers, scribes and priests) were aware of this shortcoming – but they came up with a way to circumvent this problem: instead of learning an operation, or a formula that could calculate the sides from the area, they calculated the area for all possible sides and shapes of …

## What is the nature of quadratic equation?

A quadratic equation is an equation of degree 2 in the form ax²+bx+c = 0, where a is not equal to 0. The value of x in this equation is called the roots of the quadratic equation. There are only two roots in a quadratic equation. The nature of these roots can be real and imaginary.

### What are the three types of roots in quadratic equation?

Types of roots of a Quadratic Equation

- (i) Rational and Distinct.
- (ii) Rational and Equal.
- (iii) Irrational numbers ( Conjugate irrational numbers )
- (iv) Complex numbers ( Conjugate complex numbers )

**How are quadratic functions used in solving real life problems and in making decisions?**

Quadratic equations are actually used in everyday life, as when calculating areas, determining a product’s profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.

**What is the importance of roots of quadratic equation?**

The physical significance of the roots is that at the roots of an equation, the graph of the equation intersects x-axis. The x-axis represents the real line in the Cartesian plane. This means that if the equation has unreal roots, it won’t intersect x-axis and hence it cannot be written in factorized form.

## Why is it called the quadratic formula?

This is the case because quadratum is the Latin word for square, and since the area of a square of side length x is given by x2, a polynomial equation having exponent two is known as a quadratic (“square-like”) equation.