### 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

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