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

Question 1:

Solve the equation x2 + 3 = 0

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

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

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

The given quadratic equation is –x2 + – 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

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

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

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

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

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