RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 11 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 11. Students can also read RBSE Class 11 Maths Important Questions for exam preparation. Students can also go through RBSE Class 11 Maths Notes to understand and remember the concepts easily.

RBSE Class 11 Maths Solutions Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 1.
x2 + 3 = 0
Answer:
Given equation: x2 + 3 = 0
or x2 = - 3
∴ x = ± √- 3
= ± √3 (- 1)
= ± √3 √- 1
= ± √3i (∵ √- 1 = i)
Thus, solution of equation x = √3i and x = - √3i

RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 2.
2x2 + x + 1 = 0
Answer:
Given equation 2x2 + x + 1 = 0
Comparing with ax2 + bx + c = 0
Discriminant of given equation = b2 - 4ac
D = 12- 4 × 2 × 1
= 1 - 8
D = - 7 < 0
Thus, solution of equation
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 1
(positive and negative values are taken separately)

Question 3.
x2 + 3x + 9 = 0
Answer:
Given equation: x2 + 3x + 9=0.
On comparing with ax2 + bx + c = 0
Here, a = 1, b = 3, c = 9
Here, discriminant of equation = b2 - 4ac
D = 9 - 4 × 1 × 9
D = 9 - 36
D = - 27 < 0
Then solution of equation
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 2

RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 4.
- x2 + x - 2 = 0
Answer:
Given equation: - x2 + x - 2 = 0,
On comparing with ax2 + bx + c = 0
Here, a = - 1, b = 1, c = - 2
Discriminant for given equation,
= b2 - 4ac
=12 - 4 × (- 1) (- 2)
= 1 - 8
D = - 7 < 0,
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 3

Question 5.
x2 + 3x + 5 = 0
Answer:
Given equation: x2 + 3x + 5 = 0
On comparing with ax2 + bx + c = 0
Here, a = 1, b = 3, c = 5
Discriminant of equation = b2 - 4ac
= 32 - 4 × 1 × 5
= 9 - 20
D = - 11 < 0
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 4

RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 6.
x2 - x + 2 = 0
Answer:
Given equation: x2 - x + 2 = 0
Comparing with ax2 + bx + c = 0
Here, a = !1, b = - 1, c = 2
Discriminant of equation,
= b2 - 4ac
= (- 1)2 - 4 × 1 × 2
= 1 - 8
D = - 7 < 0
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 5

Question 7.
√2x2 + x + √2 = 0
Answer:
Given equation: √2x2 + x + √2 = 0
On comparing with ax2 + bx + c = 0
Here, a = √2, b = 1, c = √2
Discriminant of equation = b2 - 4ac
= 12 - 4 × √2 × √2
= 1 - 8
D = - 7 < 0
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 6

RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 8.
√3x2 - √2x + 3√3 = 0
Answer:
Given equation: √3x2 - √2x + 3√3 = 0
On comparing with ax2 + bx + c = 0
Here, a = √3, b = - √2, c = 3√3
Discriminant of equation = b2 - 4ac
= (- √2)2 - 4 × √3 × 3√3
= 2 - 4 × 3 × 3 = 2 - 36
D = - 34 < 0
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 7

Question 9.
x2 + x + \(\frac{1}{\sqrt{2}}\) = 0
Answer:
Given equation: x2 + x + \(\frac{1}{\sqrt{2}}\) = 0
On comparing with ax2 + bx + c = 0
Here, a = 1, b = 1, c = \(\frac{1}{\sqrt{2}}\)
Discriminant of equation = b2 - 4ac
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 8

RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3

Question 10.
x2 + \(\frac{x}{\sqrt{2}}\) + 1 = 0
Answer:
Given equation: x2 + \(\frac{x}{\sqrt{2}}\) + 1 = 0
On comparing with ax2 + bx + c = 0
Here, a = 1, b = \(\frac{1}{\sqrt{2}}\) and c = 1
Discriminant of equation = b2 - 4ac
RBSE Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 9

Bhagya
Last Updated on Dec. 14, 2022, 10:42 a.m.
Published Dec. 13, 2022