Quadratic Equations Class 10
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A quadratic equation is a second-degree polynomial equation in a single variable x, with the general form:
ax^2 + bx + c = 0
where a, b, and c are constants with a
eq 0.
Quadratic Formula
The quadratic formula is used to find the solutions (or roots) of a quadratic equation. The solutions are given by:
x = (-b ± √(b^2 - 4ac))/ 2a
Here, the term under the square root, b^2 - 4ac, is known as the discriminant (D)
Nature of Roots
The nature of the roots of a quadratic equation depends on the value of the discriminant (D):
1. Real and Distinct Roots: If D is greater than 0, the quadratic equation has two distinct real roots.
2. Real and Equal Roots: If D = 0, the quadratic equation has exactly one real root (also called a repeated or double root).
3. Complex Roots: If D is less than 0, the quadratic equation has two complex conjugate roots.
In summary, the quadratic equation, quadratic formula, and the nature of its roots are fundamental concepts in algebra that describe how to find and interpret the solutions of second-degree polynomial equations.
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