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

#### Page No 109:

#### Question 1:

Solve the equation

*x*^{2}+ 3 = 0#### Answer:

The given quadratic equation is

*x*^{2}+ 3 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= 1,

*b*= 0, and

*c*= 3

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 0^{2}– 4 × 1 × 3 = –12
Therefore, the required solutions are

#### Question 2:

Solve the equation 2

*x*^{2}+*x*+ 1 = 0#### Answer:

The given quadratic equation is 2

*x*^{2}+*x*+ 1 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= 2,

*b*= 1, and

*c*= 1

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 1^{2}– 4 × 2 × 1 = 1 – 8 = –7
Therefore, the required solutions are

#### Question 3:

Solve the equation

*x*^{2}+ 3*x*+ 9 = 0#### Answer:

The given quadratic equation is

*x*^{2}+ 3*x*+ 9 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= 1,

*b*= 3, and

*c*= 9

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 3^{2}– 4 × 1 × 9 = 9 – 36 = –27
Therefore, the required solutions are

#### Question 4:

Solve the equation –

*x*^{2}+*x*– 2 = 0#### Answer:

The given quadratic equation is –

*x*^{2}+*x*– 2 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= –1,

*b*= 1, and

*c*= –2

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 1^{2}– 4 × (–1) × (–2) = 1 – 8 = –7
Therefore, the required solutions are

#### Question 5:

Solve the equation

*x*^{2}+ 3*x*+ 5 = 0#### Answer:

The given quadratic equation is

*x*^{2}+ 3*x*+ 5 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= 1,

*b*= 3, and

*c*= 5

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 3^{2}– 4 × 1 × 5 =9 – 20 = –11
Therefore, the required solutions are

#### Question 6:

Solve the equation

*x*^{2}–*x*+ 2 = 0#### Answer:

The given quadratic equation is

*x*^{2}–*x*+ 2 = 0
On comparing the given equation with

*ax*^{2}+*bx*+*c*= 0, we obtain*a*= 1,

*b*= –1, and

*c*= 2

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= (–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

*ax*^{2}+*bx*+*c*= 0, we obtain*a*=,

*b*= 1, and

*c*=

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*= 1^{2}– = 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

*ax*^{2}+*bx*+*c*= 0, we obtain*a*=,

*b*=, and

*c*=

Therefore, the discriminant of the given equation is

D =

*b*^{2}– 4*ac*=
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

*ax*^{2}+*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

*ax*^{2}+*bx*+*c*= 0, we obtain*a*=,

*b*= 1, and

*c*=

Therefore, the required solutions are

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