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Solve the equation x2 + 3 = 0
The given quadratic equation is x2 + 3 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 0, and c = 3
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 02 – 4 × 1 × 3 = –12
Therefore, the required solutions are
Solve the equation 2x2 + x + 1 = 0
The given quadratic equation is 2x2 + x + 1 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 2, b = 1, and c = 1
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 4 × 2 × 1 = 1 – 8 = –7
Therefore, the required solutions are
Solve the equation x2 + 3x + 9 = 0
The given quadratic equation is x2 + 3x + 9 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 3, and c = 9
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 32 – 4 × 1 × 9 = 9 – 36 = –27
Therefore, the required solutions are
Solve the equation –x2 + x – 2 = 0
The given quadratic equation is –x2 + x – 2 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = –1, b = 1, and c = –2
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 4 × (–1) × (–2) = 1 – 8 = –7
Therefore, the required solutions are
Solve the equation x2 + 3x + 5 = 0
The given quadratic equation is x2 + 3x + 5 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = 3, and c = 5
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 32 – 4 × 1 × 5 =9 – 20 = –11
Therefore, the required solutions are
Solve the equation x2 – x + 2 = 0
The given quadratic equation is x2 – x + 2 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain
a = 1, b = –1, and c = 2
Therefore, the discriminant of the given equation is
D = b2 – 4ac = (–1)2 – 4 × 1 × 2 = 1 – 8 = –7
Therefore, the required solutions are
Solve the equation 
The given quadratic equation is
On comparing the given equation with ax2 + bx + c = 0, we obtain
a =
, b = 1, and c =
Therefore, the discriminant of the given equation is
D = b2 – 4ac = 12 – 
= 1 – 8 = –7
Therefore, the required solutions are
Solve the equation 
The given quadratic equation is
On comparing the given equation with ax2 + bx + c = 0, we obtain
a =
, b =
, and c =
Therefore, the discriminant of the given equation is
D = b2 – 4ac =
Therefore, the required solutions are
Solve the equation
The given quadratic equation is
This equation can also be written as 
On comparing this equation with ax2 + bx + c = 0, we obtain
a =
, b =, and c = 1
Therefore, the required solutions are
Solve the equation 
The given quadratic equation is
This equation can also be written as
On comparing this equation with ax2 + bx + c = 0, we obtain
a =
, b = 1, and c =
Therefore, the required solutions are
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