- Solve the equation x2 + 3 = 0
Solution:
The given quadratic equation is x2 + 3 = 0
On comparing the given equation with ax2 + bx + c = 0,
we get a = 1, b = 0, and c = 3
Discriminant D = b2 – 4ac = 02 – 4 × 1 × 3 = –12
Therefore, the required solutions are
-b ± √D/2a = ± √-12/2×1 = ± √12 i/2 = ± 2√3i/2 = ±√3i
2: Solve the equation 2x2 + x + 1 = 0
Solution:
The given quadratic equation is 2x 2 + x + 1 = 0
On comparing the given equation with ax2 + bx + c = 0,
we get a = 2, b = 1, and c = 1
Discriminant D = b2 – 4ac = 12 – 4 × 2 × 1 = 1 – 8 = –7
Therefore, the required solutions are
-b ± √D/2a = 1± √-7/2×2 = -1 ± √7 i/2×2 = -1 ± √7i/4
- Solve the equation x2 + 3x + 9 = 0
Solution:
The given quadratic equation is x 2 + 3x + 9 = 0
On comparing the given equation with ax2 + bx + c = 0,
we obtain a = 1, b = 3, and c = 9
Discriminant D = b2 – 4ac = 32 – 4 × 1 × 9 = 9 – 36 = –27
Therefore, the required solutions are
-b ± √D/2a = -3 ± √-27/2×1 = -3 ± 3√-3/2 = -3 ± 3√3i/2
4: Solve the equation –x 2 + x – 2 = 0
Solution:
The given quadratic equation is –x 2 + x – 2 = 0
On comparing the given equation with ax2 + bx + c = 0,
we obtain a = –1, b = 1, and c = –2
Discriminant D = b2 – 4ac = 12 – 4 × (–1) × (–2) = 1 – 8 = –7
Therefore, the required solutions are
-b ± √D/2a = -1 ± √-7/2x(-1) = -1 ± √7 i/2
- Solve the equation x2 + 3x + 5 = 0
Solution:
The given quadratic equation is x 2 + 3x + 5 = 0
On comparing the given equation with ax2 + bx + c = 0,
we get a = 1, b = 3, and c = 5
Discriminant D = b2 – 4ac = 32 – 4 × 1 × 5 =9 – 20 = –11
Therefore, the required solutions are
-b ± √D/2a = -3 ± √-11/2×1 = -3 ± √11 i/2
6: Solve the equation x 2 – x + 2 = 0
Solution:
The given quadratic equation is x 2 – x + 2 = 0
On comparing the given equation with ax2 + bx + c = 0, we obtain a = 1, b = –1, and c = 2
Discriminant D = b2 – 4ac = (–1)2 – 4 × 1 × 2 = 1 – 8 = –7
Therefore, the required solutions are
-b ± √D/2a = -(-1) ± √-7/2×1 = 1 ± √12 i/2
- Solve the equation √2x2 + x+ √2 = 0
Solution:
The given quadratic equation is √2x2 + x+ √2 = 0
On comparing the given equation with ax2 + bx + c = 0,
we get a =√2 , b = 1, and c = √2
Discriminant D = b2 – 4ac = 12 – = 1 – 8 = –7
Therefore, the required solutions are
-b ± √D/2a = -1 ± √-7/2×1 = -1 ± √7 i/2
8: Solve the equation √3x2 – √2x + 3√3 = 0
Solution:
The given quadratic equation is √3x2 – √2x + 3√3 = 0
On comparing the given equation with ax2 + bx + c = 0,
we have 𝑎 = √3, 𝑏 = −√2 𝑎𝑛𝑑 𝑐 = 3√3
Discriminant D = b2 – 4ac = (-√2)2 – 4(√3)(3√3) = 2 – 36 = -34
Therefore, the required solutions are
-b ± √D/2a = -(-√2) ± √-34/2×1 = -(-√2) ± √34i/2
- Solve the equation x2 + x + 1/√2 = 0
Solution:
The given quadratic equation x2 + x + 1/√2 = 0
x2 + x + 1/√2 = √2x2 + √2x + 1 = 0
On comparing this equation with ax2 + bx + c = 0, we get 𝑎 = √2, 𝑏 = √2 𝑎𝑛𝑑 𝑐 = 1
Discriminant (D) = b2 – 4ac = (√2)2 – 4 (√2)x1 = 2 – 4√2
Therefore, the required solutions are
-b ± √D/2a = -√2 ± √[2-4√2] /2x√2 = -√2 ± √[2(1-2√2] /2x√2 = [[-√2 ±√2(√(2√2-1)]i/2x√2] = -1±(√2(√2-1))i/2
- Solve the equation x2 + x/√2 + 1 = 0
Solution:
The given quadratic equation is x2 + x/√2 + 1 = 0
x2 + x/√2 + 1 = √2x2 + x + √2 = 0
On comparing this equation with ax2 + bx + c = 0, we obtain 𝑎 = √2, 𝑏 = 1 𝑎𝑛𝑑 𝑐 = √2
Discriminant D = b2 – 4ac = 12 – 4√2x√2 = 1 – 8 = -7
Therefore, the required solutions are
-b ± √D/2a = -1 ± √-7/2x√2 = -1 ± √7 i/2√2
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