### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Fundamental Theorem of Algebra “Every Polynomial equation of degree has at least on root in  More specifically we have, “Every Polynomial equation of degree has roots in So, now the equation has two roots:  In a quadratic equation with real coefficients complex roots occur in conjugate pairs.

Example 1:

Solve: Solution: , Here,   Example 2:

Solve: Here   Example 3:

Solve:     Application

(i) General Solution of the equation: is a positive integer  , where So, general solution of the equation , where ‘ ‘ is a complex number, and , then the ‘ ‘ solutions are where (ii) Finding square roots of a complex number Let , where  So, we have two roots,    Hence and Example:

Obtain the square roots of Solution:

Let , such that , then  Now, Since is non-negative, we have  Hence the square roots of are and Scroll to Top