# Math Book 1: Quadratic Equations

Algebra - Quadratic Equations

Quadratic Equations in Algebra is a topic from which you could expect 2 to 3 questions in the GMAT quant section. The topic is an important one. Many questions that appear in this topic are word problems that expect you to write an equation from the information given and then solve it. The gist of what is tested is your ability to write the equation appropriately.

### Concepts Covered

Quadratic Equations or equations of the second order where the variables have a power of 2 and are of the form ax2 + bx + c = 0. Solutions or roots of a quadratic equation, types of roots of quadratic equations. Factorizing a quadratic equation to find its solutions is also tested in GMAT. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Introduction to quadratic equations and roots of quadratic equations.
2. Concept of discriminant of quadratic equation.
3. Method to calculate the sum, difference and product of roots along with illustrative examples.
4. Method to form a quadratic equation, given its roots; explained with illustrative examples.
5. Definition of conjugate roots.
6. Concepts in quadratic equations such as common roots, minimum and maximum value of quadratic equations.
7. Method to determine nature of roots (real, rational, equal, imaginary), and their relation to the discriminant of the equation.
8. Method to determine the value and sign of roots using value and sign of the coefficients of the quadratic equation.
9. What does a quadratic equation equation represent when plotted on an x-y plane?
10. Types of curves for different values of the discriminant; when b2 - 4ac > 0; when b2 - 4ac = 0; when b2 - 4ac < 0
11. 16 solved examples to explain above mentioned concepts.
12. 18 exercise problems with the answer key and detailed explanatory answers.
13. A multiple choice test with 34 questions from linear and quadratic equations along with explanatory answers and answer key as part of the work book.

Here is a typical solved example from this chapter.

### Sample Question

The area of a right triangle is 30 sq units. What are its base and altitude if the altitude exceeds the base by 7 units?

Step 1: Frame an equation with the information given in the question.

Let the base of the triangle be 'b' units and the altitude be 'h' units

Altitude exceeds the base by 7 units: i.e., h = b + 7

Area of the right triangle = 30 sq units.
Area of a right triangle = $$frac{1}{2}\\$ * b * h $\frac{1}{2}\\$ * b *$b + 7) = 30
b(b + 7) = 60
b2 + 7b - 60 = 0

Step 2: Factorize and solve the equation to find 'b'.

b2 + 12b - 5b - 60 = 0
b(b + 12) -5(b + 12) = 0
(b + 12)(b - 5) = 0
(b + 12) = 0 or (b - 5) = 0
b = -12 or b = 5

Measures of length of sides of triangles are always positive. So, b = 5

The altitude 'h' = (b + 7) = 5 + 7 = 12.

base = 5 units and altitude = 12 units

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details