## EXERCISE 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