Question:
$x^{2}+2 x+2=0$
Solution:
Given:
$x^{2}+2 x+2=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-2 \pm \sqrt{(2)^{2}-(4 \times 1 \times 2)}}{2 \times 1}$
$\Rightarrow x=\frac{-2 \pm \sqrt{4-8}}{2}$
$\Rightarrow \quad x=\frac{-2 \pm \sqrt{-4}}{2}$
$\Rightarrow x=\frac{-2 \pm 2 i}{2}$
$\Rightarrow x=-\frac{2}{2} \pm \frac{2}{2} i$
$\Rightarrow^{x}=-1 \pm i$
Ans: $x=-1+i$ and $x=-1-i$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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