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

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

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

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

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

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

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

Question 7:

Solve the equation 

Answer:

The given quadratic equation is

On comparing the given equation with ax² + bx + c = 0, we obtain

a =, b = 1, and c =

Therefore, the discriminant of the given equation is

D = b² – 4ac = 1² – = 1 – 8 = –7

Therefore, the required solutions are

Question 8:

Solve the equation 

Answer:

The given quadratic equation is

On comparing the given equation with ax² + bx + c = 0, we obtain

a =, b =, and c =

Therefore, the discriminant of the given equation is

D = b² – 4ac =

Therefore, the required solutions are

Question 9:

Solve the equation

Answer:

The given quadratic equation is

This equation can also be written as 

On comparing this equation with ax² + bx + c = 0, we obtain

a =, b =, and c = 1

Therefore, the required solutions are

Question 10:

Solve the equation 

Answer:

The given quadratic equation is

This equation can also be written as

On comparing this equation with ax² + bx + c = 0, we obtain

a =, b = 1, and c =

Therefore, the required solutions are