# 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

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

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

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.

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.

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

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

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

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