NCERT SOLUTIONS FOR CLASS 11 MATHS CHAPTER 5 / COMPLEX NUMBERS AND QUADRATIC EQUATIONS EX 5.3 /

Solve each of the following equations.

Question 1. x2 + 3 = 0

Solution.

We have, x2 + 3 = 0 ⇒ x2 = -3

⇒ x=\pm \sqrt { -3 }  ⇒ x = \pm \sqrt { 3 } i

Question 2. 2x2 + x + 1 = 0

Solution.

We have, 2x2 + x + 1 = 0

Comparing the given equation with the general form ax2 + bx + c = 0, we get

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 1

Question 3. x2 + 3x + 9 = 0

Solution.

We have, x2 + 3x + 9 = 0

Comparing the given equation with the general form ax2 + bx + c = 0,we get a = 1, b = 3, c = 9

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 2

Question 4. -x2 + x – 2 = 0

Solution.

We have, -x2 + x – 2 = 0

Comparing the given equation with the general form ax2 + bx + c = 0,we get

a = 1, b = 1, c = -2

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 3

Question 5. x2 + 3x + 5 = 0

Solution.

We have, x2 + 3x + 5 = 0

Comparing the given equation with the general form ax2 + bx + c = 0, we get a = 1, b = 3, c = 5.

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 4

Question 6. x2 – x + 2 = 0

Solution.

We have, x2 – x + 2 = 0

Comparing the given equation with the general form ax2 + bx + c = 0, we get a = 1, b = -1, c = 2.

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

Question 7.

\sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0

Solution.

We have, \sqrt { 2 } { x }^{ 2 }+x+\sqrt { 2 } =0

Comparing the given equation with the general form ax2 + bx + c = 0, we get

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 6

Question 8.

\sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0

Solution.

We have, \sqrt { 3 } { x }^{ 2 }+\sqrt { 2 } x+3\sqrt { 3 } =0

Comparing the given equation with the general form ax2 + bx + c = 0, we get

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 7

Question 9.

{ x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0

Solution.

We have, { x }^{ 2 }+x+\frac { 1 }{ \sqrt { 2 } } =0

Comparing the given equation with the general form ax2 + bx + c = 0, we get

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 8

Question 10.

{ x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0

Solution.

We have, { x }^{ 2 }+\frac { x }{ \sqrt { 2 } } +1=0

Comparing the given equation with the general form ax2 + bx + c = 0, we get

NCERT Solutions for Class 11 Maths Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 9