Chapter 5 Complex Numbers and Quadratic Equations Ex 5.3 Solutions
Question - 1 : - Solve the equation x2 + 3 = 0
Answer - 1 : -
Given quadratic equation,
x2 + 3 = 0
On comparing it with ax2 + bx + c =0, we have
a =1, b =0, and c =3
So, the discriminant of the given equation will be
D = b2 –4ac =02 – 4 × 1 × 3 = –12
Hence, the required solutions are:
Question - 2 : - 2x2 + x + 1 = 0
Answer - 2 : -
Given quadratic equation,
2x2 + x +1 = 0
On comparing it with ax2 + bx + c =0, we have
a =2, b =1, and c =1
So, the discriminant of the given equation will be
D = b2 –4ac =12 – 4 × 2 × 1 = 1 – 8 = –7
Hence, the required solutions are:
Question - 3 : - x2 + 3x + 9 = 0
Answer - 3 : -
Given quadratic equation,
x2 + 3x + 9 = 0
On comparing it with ax2 + bx + c =0, we have
a =1, b =3, and c =9
So, the discriminant of the given equation will be
D = b2 –4ac =32 – 4 × 1 × 9 = 9 – 36 = –27
Hence, the required solutions are:
Question - 4 : - –x2 + x – 2 = 0
Answer - 4 : -
Given quadratic equation,
–x2 + x –2 = 0
On comparing it with ax2 + bx + c =0, we have
a =–1, b =1, and c =–2
So, the discriminant of the given equation will be
D = b2 –4ac =12 – 4 × (–1) × (–2) = 1 – 8 =–7
Hence, the required solutions are:
Question - 5 : - x2 + 3x + 5 = 0
Answer - 5 : -
Given quadratic equation,
x2 + 3x + 5 = 0
On comparing it with ax2 + bx + c =0, we have
a =1, b =3, and c =5
So, the discriminant of the given equation will be
D = b2 –4ac =32 – 4 × 1 × 5 =9 – 20 = –11
Hence, the required solutions are:
Question - 6 : - x2 – x + 2 = 0
Answer - 6 : -
Given quadratic equation,
x2 – x + 2 = 0
On comparing it with ax2 + bx + c =0, we have
a =1, b =–1, and c =2
So, the discriminant of the given equation is
D = b2 –4ac =(–1)2 – 4 × 1 × 2 = 1 – 8 = –7
Hence, the required solutions are
Question - 7 : - √2x2 + x + √2 = 0
Answer - 7 : -
Given quadratic equation,
√2x2 + x +√2 = 0
On comparing it with ax2 + bx + c =0, we have
a =√2, b =1, and c =√2
So, the discriminant of the given equation is
D = b2 –4ac =(1)2 – 4 × √2 × √2 = 1 – 8 = –7
Hence, the required solutions are:
Question - 8 : - √3x2 – √2x + 3√3 = 0
Answer - 8 : -
Given quadratic equation,
√3x2 –√2x +3√3 = 0
On comparing it with ax2 + bx + c =0, we have
a =√3, b =-√2, and c =3√3
So, the discriminant of the given equation is
D = b2 –4ac =(-√2)2 – 4 × √3 × 3√3 = 2 – 36 =–34
Hence, the required solutions are:
Question - 9 : - x2 + x + 1/√2 = 0
Answer - 9 : -
Given quadratic equation,
x2 + x + 1/√2 = 0
It can be rewritten as,
√2x2 +√2x +1 = 0
On comparing it with ax2 + bx + c =0, we have
a =√2, b =√2, and c =1
So, the discriminant of the given equation is
D = b2 –4ac =(√2)2 – 4 × √2 × 1 = 2 – 4√2 =2(1 – 2√2)
Hence, the required solutions are:
Question - 10 : - x2 + x/√2 + 1 = 0
Answer - 10 : -
Given quadratic equation,
x2 + x/√2 + 1 = 0
It can be rewritten as,
√2x2 + x +√2 = 0
On comparing it with ax2 + bx + c =0, we have
a =√2, b =1, and c =√2
So, the discriminant of the given equation is
D = b2 –4ac =(1)2 – 4 × √2 × √2 = 1 – 8 = -7
Hence, the required solutions are:
