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# Quadratic Equation for Class 10

A quadratic equation is a second-degree polynomial equation of the form: ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The term "quadratic" comes from the Latin word "quadratus," which means "square."

The quadratic equation is an important topic in mathematics and has many applications in different fields. Some examples of real-world problems that can be modeled using quadratic equations are finding the maximum or minimum value of a parabolic curve, determining the time it takes for an object to hit the ground when thrown from a certain height, or calculating the area of a rectangle with a known perimeter.

To solve a quadratic equation, there are different methods that can be used, including factoring, completing the square, and using the quadratic formula. These methods allow us to find the values of x that make the equation true, which are also known as the roots or solutions of the equation.

The quadratic formula is a general method for solving any quadratic equation and is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

where ± indicates that we need to take both the positive and negative roots, and √ represents the square root function. This formula works for all quadratic equations, regardless of the values of a, b, and c.

In summary, the quadratic equation is a powerful mathematical tool that allows us to model and solve real-world problems using second-degree polynomial equations.

### Quadratic Equation for Class 10

The quadratic equation is an important topic in mathematics, and it is commonly studied in Class 10. The standard form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants, and x is the variable.

To solve a quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where ± indicates that we need to take both the positive and negative roots, and √ represents the square root function.

To use the quadratic formula, we need to first identify the values of a, b, and c from the given equation. Once we have these values, we can substitute them into the formula and solve for x.

For example, let's say we have the quadratic equation:

2x^2 + 5x - 3 = 0

Here, a = 2, b = 5, and c = -3. Substituting these values into the quadratic formula, we get:

x = (-5 ± √(5^2 - 4(2)(-3))) / 2(2)

Simplifying the equation, we get:

x = (-5 ± √49) / 4

x = (-5 ± 7) / 4

So, the roots of the quadratic equation are:

x = (-5 + 7) / 4 = 1/2 or x = (-5 - 7) / 4 = -3

Therefore, the solutions of the given quadratic equation are x = 1/2 and x = -3.

So that's the article about "Quadratic Equation for Class 10" along with questions and answers, as well as explanations. Those are the articles that Kimtuck.com can share, and we hope they are useful.