# Important Questions for Class 11 Chapter 5 - Complex number and Quadratic Equations

The CBSE Important Question for all the subjects from grades 6th to 10th will help you in preparing for exams,solving homework questions or learning concepts as well.The complete set of important questions for CBSE class 11th Maths prepared by our subject experts contains all the explanations and step by step solutions for the chapters and topics in Maths.

**Important questions based on NCERT syllabus for Class 11 Chapter 5-Complex number and Quadratic Equations:**

*Question 1*: let 2x^2 + 3x + 8 = 0. Without computing the roots find

i) 1/α + 1/β

ii) α^2 + β^2

iii) α^3 + β^3

*Solution*:

Let α and β be the roots of the equation

sum of the roots α + β = -b/a = -3/2

product of the roots αβ = c/a = 8/2 = 4

i) 1/α + 1/β = α + β/αβ [ by taking LCM]

Substitute vales of α + β and αβ in the above we get

-3/2/4 = -3/2 x 1/4= -3/8

ii) α^2 + β^2 = (α + β)^2 - 2αβ

= (-3/2)^2 - 2(4)

= 9/4 - 8

= (9-32)/4

= -23/4

iii) α^3 + β^3 = (α + β)^3 - 3αβ(α + β)

= (-3/2)^3 -3(4)(-3/2)

= 27/8 - 18

= 27-144/8

= 117/8

*Question 2*: Find (i+2)^2

*Solution*: We know that (a+b)^2 = a^2 + b^2 +2ab

i^2 + 2^2 + 2(i)2 [i^2 = 1]

= 1 + 4 + 4i

= 4i + 5

*Question 3*: Find the sum of the roots of the equation x^2 + x+ 1 = 0

*Solution*:

Given x^2 + x+ 1 = 0

we apply the formula to find the roots of the equation.

x = -b ±√ (b^2 - 4ac)/2ab

here b = 1 a = 1 c = 1

Substitute to get the roots

x = -1± √(1 - 4(1)1))/2(1) = (-1 ± √(1 - 4))/2 = -1 ±√-3)/2 = -1±3i/2

Hence the roots of equation -1+3i/2, -1-3i/2