Question:
$3 x^{2}-4 x+\frac{20}{3}=0$
Solution:
Given:
$3 x^{2}-4 x+\frac{20}{3}=0$
Multiplying both the sides by 3 we get,
$9 x^{2}-12 x+20=0$
Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:
$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$
$\Rightarrow x=\frac{-(-12) \pm \sqrt{(-12)^{2}-(4 \times 9 \times 20)}}{2 \times 9}$
$\Rightarrow x=\frac{12 \pm \sqrt{144-720}}{18}$
$\Rightarrow x=\frac{12 \pm \sqrt{-576}}{18}$
$\Rightarrow x=\frac{12 \pm 24 i}{18}$
$x=\frac{12}{18} \pm \frac{24}{18} i$
$\Rightarrow \quad x=\frac{2}{3} \pm \frac{4}{3} i$
Ans: $x=\frac{2}{3}+\frac{4}{3} i$ and $x=\frac{2}{3}-\frac{4}{3} i$
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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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