Quadratic Equations

Formulas are organized based on their importance in the CAT exam.
1 Minimum and Maximum of Quadratic on an Interval
2 Quadratic in Completed Square Form
3 Common Root of Two Quadratics
4 Transformed Roots: Scaled Roots
5 Quadratic Expression with a Fixed Sign
6 Sum of squares of roots
7 Condition for Positive Roots
8 Difference of roots
9 Roots Shifted by a Constant
10 Quadratic formula (roots)
11 Condition for Equal Roots
12 Maximum and Minimum Value
13 Discriminant
14 Difference of Powers of Roots
15 Transformed Roots: Reciprocal
16 Roots in an Interval
17 Recurrence Relation for Powers of Roots
18 Quadratic Expression Never Zero
19 Location of Roots
20 Equation with Given Roots
21 AM-GM Form of a Quadratic
22 Quadratic Function
23 Common Roots of Two Quadratics
24 Roots Decreased by a Constant
25 Biquadratic reduction
26 Condition for a Given Number to Be a Root
27 Condition for Negative Roots
28 Range of a Quadratic Function
29 Sum and Product of Roots
30 Quadratic Through Given Points
31 Expressions Involving Reciprocal Roots
32 Location of Roots Relative to a Point
33 Nature of Roots
34 Vertex and Roots Relationship
35 Equation with Roots in Terms of Given Roots
36 Intercepts of a Quadratic
37 Quadratic Equation with Parameter
38 Discriminant
39 Quadratic with Roots $$\alpha$$ and $$\beta$$
40 Reciprocal Root Relations
41 Transformed Roots: Negative Roots
42 Relation Between Roots and Constant Term
43 Minimum Value of a Quadratic Expression
44 Quadratic Inequalities
45 Sign of a Quadratic
46 Quadratic Equation from Sum and Product
47 Quadratic with Known Roots
48 Relation Between Roots and Graph
49 Quadratic Expression Always Negative
50 Relation Between Roots and Linear Coefficient
51 Condition for Roots of Opposite Signs
52 Difference of Roots
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 Condition for equal roots
62 Relation Between Coefficients and Vertex
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