Question:
Solve the equation $x^{2}+x+\frac{1}{\sqrt{2}}=0$
Solution:
The given quadratic equation is $x^{2}+x+\frac{1}{\sqrt{2}}=0$
This equation can also be written as $\sqrt{2} x^{2}+\sqrt{2} x+1=0$
On comparing this equation with $a x^{2}+b x+c=0$, we obtain
$a=\sqrt{2}, b=\sqrt{2}$, and $c=1$
$\therefore$ Discri min ant $(D)=b^{2}-4 a c=(\sqrt{2})^{2}-4 \times(\sqrt{2}) \times 1=2-4 \sqrt{2}$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-\sqrt{2} \pm \sqrt{2-4 \sqrt{2}}}{2 \times \sqrt{2}}=\frac{-\sqrt{2} \pm \sqrt{2(1-2 \sqrt{2})}}{2 \sqrt{2}}$
$=\left(\frac{-\sqrt{2} \pm \sqrt{2}(\sqrt{2 \sqrt{2}-1}) \mathrm{i}}{2 \sqrt{2}}\right) \quad[\sqrt{-1}=\mathrm{i}]$
$=\frac{-1 \pm(\sqrt{2 \sqrt{2}-1}) i}{2}$
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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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