NCERT Solutions for Class 11 Maths Chapter 5 – Complex Numbers and Quadratic Equations Ex 5.3
Page No 109:
Question 1:
Solve the equation x2 + 3 = 0
Answer:
The given quadratic equation is x2 + 3 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 0, and c = 3
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 02 – 4 × 1 × 3 = –12
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4142/CHAPTER%205_html_m3a3be76b.gif)
Question 2:
Solve the equation 2x2 + x + 1 = 0
Answer:
The given quadratic equation is 2x2 + x + 1 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 2, b = 1, and c = 1
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 4 × 2 × 1 = 1 – 8 = –7
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4143/CHAPTER%205_html_m4a67dc8f.gif)
Question 3:
Solve the equation x2 + 3x + 9 = 0
Answer:
The given quadratic equation is x2 + 3x + 9 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 3, and c = 9
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 32 – 4 × 1 × 9 = 9 – 36 = –27
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4144/CHAPTER%205_html_c1e98c5.gif)
Question 4:
Solve the equation –x2 + x – 2 = 0
Answer:
The given quadratic equation is –x2 + x – 2 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = –1, b = 1, and c = –2
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 4 × (–1) × (–2) = 1 – 8 = –7
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4145/CHAPTER%205_html_78ce8dee.gif)
Question 5:
Solve the equation x2 + 3x + 5 = 0
Answer:
The given quadratic equation is x2 + 3x + 5 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 3, and c = 5
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 32 – 4 × 1 × 5 =9 – 20 = –11
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4146/CHAPTER%205_html_32801ea2.gif)
Question 6:
Solve the equation x2 – x + 2 = 0
Answer:
The given quadratic equation is x2 – x + 2 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = –1, and c = 2
Therefore, the discriminant of the given equation is
D = b2 – 4ac = (–1)2 – 4 × 1 × 2 = 1 – 8 = –7
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4147/CHAPTER%205_html_62a5bcd6.gif)
Question 7:
Solve the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_53aca6c2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_53aca6c2.gif)
Answer:
The given quadratic equation is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_53aca6c2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_53aca6c2.gif)
On comparing the given equation with ax2 + bx + c = 0, we obtain
a =
, b = 1, and c =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_m79f714c4.gif)
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 –
= 1 – 8 = –7
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_m79d93021.gif)
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4148/CHAPTER%205_html_18960058.gif)
Question 8:
Solve the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_412b462e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_412b462e.gif)
Answer:
The given quadratic equation is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_412b462e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_412b462e.gif)
On comparing the given equation with ax2 + bx + c = 0, we obtain
a =
, b =
, and c =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m99899c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m632093a2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m46827a9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m99899c4.gif)
Therefore, the discriminant of the given equation is
D = b2 – 4ac =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m64f15644.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_m64f15644.gif)
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4149/CHAPTER%205_html_7486a781.gif)
Question 9:
Solve the equation![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m52416dc3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m52416dc3.gif)
Answer:
The given quadratic equation is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m52416dc3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m52416dc3.gif)
This equation can also be written as ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_69522a90.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_69522a90.gif)
On comparing this equation with ax2 + bx + c = 0, we obtain
a =
, b =
, and c = 1
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m698edb5a.gif)
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/5543/Chapter%205_html_m7c8286ba.gif)
Question 10:
Solve the equation ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m673008ac.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m673008ac.gif)
Answer:
The given quadratic equation is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m673008ac.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m673008ac.gif)
This equation can also be written as![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_53aca6c2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_53aca6c2.gif)
On comparing this equation with ax2 + bx + c = 0, we obtain
a =
, b = 1, and c =![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_m79f714c4.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_37a3dd2f.gif)
Therefore, the required solutions are
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/165/4151/CHAPTER%205_html_5d702598.gif)