If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $t(t)=t^{2}-4 t+3$, find the value of $\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4} .$
Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $p(y)=t^{2}-4 t+3$
$\alpha+\beta=\frac{-\text { Coefficient of } x}{\text { Coefficient of } x^{2}}$
$=\frac{-(-4)}{1}$
= 4
$\alpha \beta=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$
$=\frac{3}{1}$
= 3
We have $\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}$
$\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}=\alpha^{3} \beta^{3}(\alpha+\beta)$
$\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}=(\alpha \beta)^{3}(\alpha+\beta)$
$\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}=(3)^{3}(4)$
$\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}=27 \times 4$
$\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}=108$
Hence, the value of $\alpha^{4} \beta^{3}+\alpha^{3} \beta^{4}$ is 108 .
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- 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,