Quadratic Equations
Quadratic Equations - JEE & CBSE
Concepts:
- Quadratic equation:
Equation in the form of
- Standard form:
Rearranged form of the equation as
- Roots of quadratic equations:
Values of
- Discriminant (D):
Quantity under the square root in the quadratic formula,
- Determines nature of roots:
- Quadratic formula:
Results:
-
Sum of roots:
-
Product of roots:
-
Special Cases:
-
Perfect square: Discriminant is a perfect square, rational equal roots
-
Incomplete quadratic equation: One variable, forms
-
Applications:
-
Solving quadratic inequalities
-
Maxima and minima problems
-
Sums of squares series
-
Problems involving quadratic relationships.
