## NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.3

Chapter 5 Complex Numbers and Quadratic Equations Exercise 5.3 is available here that will help you in solving any difficult questions present in the exercise and also for framing your own answers. Class 11 Maths NCERT Solutions given here are prepared by team of Studyrankers subject experts who have taken every care to detail every answer so students can understand the concepts easily.

1. Solve each of the following equations:

x

x

âˆ´Â x =Â Â±âˆš-3 =Â Â±âˆš3i

2. 2x

2x

a = 2, b = 1, c = 1

b

âˆ´Â x = (-bÂ Â±Â âˆš

= (-1Â Â±Â âˆš

3. x

4. -x

8. âˆš3x

We have a =Â âˆš3, b = -âˆš2, c = 3âˆš3

âˆ´Â Discriminant of the equations is D = b

ac = (-âˆš2)

=> D = 2 â€“ 36 = -34

âˆ´Â x = (-bÂ Â±Â âˆšD)/2a = (âˆš2Â Â±Â âˆš-34)/2Ã—âˆš3 = (âˆš2Â Â±Â âˆš34i)/2âˆš3

âˆ´Â x = (âˆš2Â Â±Â âˆš34i)/2âˆš3

9. x

10. x

x

we have a =Â âˆš2, b = 1, c=Â âˆš2

âˆ´Â Discriminant of the equation is

D = b

=> D = 1 â€“ 8 = -7

x

^{2}Â + 3 = 0**Answer**x

^{2}Â + 3 = 0 âˆ´Â x^{2}Â = -3âˆ´Â x =Â Â±âˆš-3 =Â Â±âˆš3i

2. 2x

^{2}Â + x + 1 = 0**Answer**2x

^{2}Â + x + 1 = 0 comparing with ax^{2}Â + bx + c = 0a = 2, b = 1, c = 1

b

^{2}Â â€“ 4ac = 1^{2}Â â€“ 4.2.1 = 1 â€“ 8 = -7âˆ´Â x = (-bÂ Â±Â âˆš

*b*^{2}*-4ac*Â )/2a = (-1Â Â±Â âˆš*-7*)/2.2= (-1Â Â±Â âˆš

*7i*)/43. x

^{2}Â + 3x + 9 = 0**Answer**4. -x

^{2}Â + x â€“ 2 = 0**Answer**
5. x

^{2}Â + 3x + 5 = 0**Answer**

6. x

^{2}Â â€“ x + 2 = 0**Answer**

7. âˆš2x

^{2}Â + x +Â âˆš2 = 0**Answer**

8. âˆš3x

^{2}Â â€“Â âˆš2x + 3âˆš3 = 0**Answer**We have a =Â âˆš3, b = -âˆš2, c = 3âˆš3

âˆ´Â Discriminant of the equations is D = b

^{2}Â â€“ 4ac = (-âˆš2)

^{2}Â â€“ 4Ã—âˆš3Ã—3âˆš3=> D = 2 â€“ 36 = -34

âˆ´Â x = (-bÂ Â±Â âˆšD)/2a = (âˆš2Â Â±Â âˆš-34)/2Ã—âˆš3 = (âˆš2Â Â±Â âˆš34i)/2âˆš3

âˆ´Â x = (âˆš2Â Â±Â âˆš34i)/2âˆš3

9. x

^{2}Â + x + 1/âˆš2 = 0**Answer**^{2}Â + x/âˆš2 + 1 = 0**Answer**x

^{2}Â + x/âˆš2 + 1 = 0 orÂ âˆš2x^{2}Â + x +Â âˆš2 = 0,we have a =Â âˆš2, b = 1, c=Â âˆš2

âˆ´Â Discriminant of the equation is

D = b

^{2}Â â€“ 4ac = 1^{2}Â â€“ 4Â Ã—Â âˆš2Â Ã—Â âˆš2=> D = 1 â€“ 8 = -7