10th Class II Revision of Quadratic Equation II NCERT Exemplar II Ex : 4.2 II PART-2

What is a Quadratic Equation?

A quadratic equation is a type of algebraic equation where the highest power of the variable (usually x) is 2.
It's often referred to as an "equation of degree 2" or a "second-degree equation".
The standard form of a quadratic equation is:
ax² + bx + c = 0
Here:
a, b, and c are constants (numbers)
a cannot be zero (because then it wouldn't be a quadratic equation)
x is the variable
Key Points

Roots or Solutions: The solutions to a quadratic equation are the values of x that make the equation true. These solutions are also called the "roots" of the quadratic equation.
Discriminant: The discriminant is a part of the quadratic formula that helps determine the nature of the roots:
If the discriminant is positive, there are two distinct real roots.
If the discriminant is zero, there is one real root (a repeated root).
If the discriminant is negative, there are no real roots (the roots are complex).
Quadratic Formula: This formula is used to find the roots of a quadratic equation:
x = (-b ± √(b² - 4ac)) / (2a)
Visual Representation

The graph of a quadratic equation is a parabola. It can open upwards or downwards, depending on the sign of the coefficient a.
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parabola opening downwards

Applications

Quadratic equations are used in various fields, including:

Physics: Projectile motion, the path of a rocket, etc.
Engineering: Bridge design, architectural structures
Economics: Modeling supply and demand curves
Mathematics: Many areas of mathematics use quadratic equations

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