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# Quadratic Equations Formulas Class 10

Quadratic equations formulas class 10 are applied to find the roots of various quadratic equations. To solve quadratic equations, students should have clarity on how to apply quadratic equations formulas in different ways to find their roots. With the list of formulas and examples presented in this article, students will clearly understand the standard form of a quadratic equation and its solutions.

## List of Quadratic Equations Formulas Class 10

Students can refer to the list of quadratic equations formulas class 10 provided below:

- A quadratic equation is represented as ax
^{2}+ bx + c = 0, where a, b, c are real numbers and a is not equal to 0. - A real number α is said to be a root of the quadratic equation ax
^{2}+ bx + c = 0, if aα^{2}+ bα + c = 0. - The roots of a quadratic equation ax
^{2}+ bx + c = 0 are: [-b±√(b²-4ac)]/(2a) if b^{2}- 4ac ≥ 0. - A quadratic equation has:

Two distinct real roots if b^{2} - 4ac >0;

Two equal roots if b^{2} - 4ac = 0;

No real roots if b^{2} - 4ac < 0.

## Applications of Quadratic Equations Formulas Class 10

Quadratic equations formulas are not just relevant in mathematics but they are also useful in many real-life situations. Thus, students should know how to apply quadratic equations formulas. Here are some examples of real-world applications of quadratic equations formulas class 10:

- Quadratic equations formulas are helpful in various engineering domains. For example, automobile engineers design brake systems in cars by applying quadratic equations formulas. Aerospace engineers also use quadratic equations formulas to determine various results.
- Quadratic equations formulas are often applied in real life to calculate the area of various objects like rooms, plots, boxes, etc. One can calculate how much grass carpet will be needed for the garden based on the information derived through these formulas.
- In business, quadratic equation functions are used to calculate business profit, loss and other related details.
- These formulas are also useful in calculating the speeds of moving objects like cars, airplanes, trains, etc. For example, traffic police use quadratic equations formulas is to determine the speeds of cars involved in accidents on the roads.

## Tips to Memorize Quadratic Equations Formulas Class 10

Here are some useful tips to help students understand and memorize quadratic equations formulas class 10:

- As there are a lot of new terms and variables involved in the quadratic expressions, hence it is important to have a clear image of them in mind. Thus, students should try to understand and learn each concept before memorizing quadratic equations class 10 formulas.

- Students should clear even the slightest doubts to get well versed in these formulas. They can make note of all their doubts and find their answers by taking help of teachers and parents.

- Students can also download study material from the internet like formula images to apply them as wallpapers or screensavers on their devices.

## Quadratic Equations Formulas Class 10 Examples

**Example 1:** Verify if (x - 1)^{2} + 2 = x - 3 is a quadratic equation.

**Solution:** Solving the equation we get, (x - 1)^{2} + 2 = x – 3

⇒ x^{2} + 1 - 2x + 2 = x - 3

⇒ x^{2} - x + 6 = 0

The given equation is of the form ax2 + bx + c = 0.

Hence, it is a quadratic equation.

**Example 2:** Find the discriminant of the quadratic equation x 2 - 3x + 3 = 0, and verify the nature of its roots.

**Solution:** The given equation is of the form ax2 + bx + c = 0, where a =1, b = -3 and c = 3.

Therefore, the discriminant d = b^{2} - 4ac

= (-3)^{2} - 4(1)(3) = 9 - 12 = - 3 < 0

Since the value of discriminant d is less than 0, the given equation has no real roots.

Students can download the printable Maths Formulas Class 10 sheet from below.

## FAQs on Quadratic Equations Formulas Class 10

### What are the Important Quadratic Equations Formulas Class 10?

The Important Quadratic Equations Formulas Class 10 are given below:

- A quadratic equation is represented as ax
^{2}+ bx + c = 0, where a, b, c are real numbers and a is not equal to 0. - A real number α is said to be a root of the quadratic equation ax
^{2}+ bx + c = 0, if

aα^{2} + bα + c = 0.

- The roots of a quadratic equation ax
^{2}+ bx + c = 0 can be found using formula: [-b±√(b²-4ac)]/(2a), if b^{2}- 4ac ≥ 0. - A quadratic equation has two distinct real roots if b
^{2}- 4ac > 0; two equal roots if b^{2}- 4ac = 0 ; no real roots if b^{2}- 4ac < 0.

### What are the Basic Concepts Related to Quadratic Equations Formulas Class 10?

The basic concepts related to quadratic equations formulas class 10 are quadratic equation in standard form, nature of roots, the value of discriminant, quadratic formula, factorization method, and square method to solve a quadratic equation.

### How Many Formulas are there in Quadratic Equations Formulas Class 10?

There are four important Quadratic Equations Formulas Class 10 as can be seen in the list given in this article. These formulas explain the nature of roots of quadratic equations. Students can have a look at the examples given in this article to have a better understanding of the same.

### How can I Memorize Quadratic Equations Formulas Class 10?

Students can memorize the Quadratic Equations Formulas Class 10 by following the tips given below:

- Students should try to write down all of the formulas, as well as their explanations. Because there are so many new terms and variables in quadratic expressions, it's crucial to have a clear picture of them in memory, which can only be done by writing.
- Seeking clarification from teachers and friends is important. Making a list of all such doubts and their answers will also help in a later revision.
- Students can also use their mobile phones by setting up formula backgrounds as screensavers. This will ensure that they get a quick glimpse of the formulas while on the go.

### How to Download Quadratic Equations Formulas Class 10 pdf?

To download quadratic equations formulas class 10 pdf students can click on the download link provided on this page. The formula sheet will provide optimal coverage to all quadratic equations formulas to learn and revise for exams.

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