Quadratic Equations

Formulas are organized based on their importance in the CAT exam.
1 Difference of roots
2 Sum of squares of roots
3 Quadratic formula (roots)
4 Quadratic Inequalities
5 Transformed Roots: Scaled Roots
6 Roots Shifted by a Constant
7 Quadratic in Completed Square Form
8 Common Root of Two Quadratics
9 Roots Decreased by a Constant
10 Difference of Powers of Roots
11 Biquadratic reduction
12 Condition for Equal Roots
13 Equation with Given Roots
14 Maximum and Minimum Value
15 Discriminant
16 Transformed Roots: Reciprocal
17 Roots in an Interval
18 AM-GM Form of a Quadratic
19 Recurrence Relation for Powers of Roots
20 Condition for Positive Roots
21 Location of Roots
22 Quadratic Expression Never Zero
23 Condition for a Given Number to Be a Root
24 Common Roots of Two Quadratics
25 Sum and Product of Roots
26 Quadratic Function
27 Quadratic Through Given Points
28 Vertex and Roots Relationship
29 Intercepts of a Quadratic
30 Equation with Roots in Terms of Given Roots
31 Condition for Negative Roots
32 Range of a Quadratic Function
33 Quadratic Equation with Parameter
34 Expressions Involving Reciprocal Roots
35 Quadratic Expression with a Fixed Sign
36 Location of Roots Relative to a Point
37 Nature of Roots
38 Discriminant
39 Quadratic with Roots $$\alpha$$ and $$\beta$$
40 Reciprocal Root Relations
41 Minimum and Maximum of Quadratic on an Interval
42 Transformed Roots: Negative Roots
43 Sign of a Quadratic
44 Relation Between Roots and Constant Term
45 Minimum Value of a Quadratic Expression
46 Quadratic Equation from Sum and Product
47 Difference of Roots
48 Quadratic with Known Roots
49 Relation Between Roots and Graph
50 Quadratic Expression Always Negative
51 Relation Between Roots and Linear Coefficient
52 Condition for Roots of Opposite Signs
53 Relation Between Roots and Coefficients Under Scaling
54 Quadratic Expression as a Perfect Square
55 Maximum Value of a Quadratic Expression
56 Quadratic Equation
57 Quadratic with Known Vertex
58 Polynomial Having Reciprocal Roots
59 Standard quadratic equation form
60 Roots on Opposite Sides of a Point
61 Relation Between Coefficients and Vertex
62 Condition for equal roots
63 Product of roots
64 Polynomial Having Square Roots of Original Roots
65 Nature of roots
66 Sum of roots
67 Sum of cubes of roots
68 Condition for Two Given Numbers to Be Roots
69 Quadratic Formula in Vertex Form
70 Symmetric Expressions in Roots
71 Complex conjugate roots
72 Formation from given roots
73 Factorization form