Question:
Find the value of $a$, if $(x+2)$ is a factor of $4 x^{4}+2 x^{3}-3 x^{2}+8 x+5 a$
Solution:
Here, $f(x)=4 x^{4}+2 x^{3}-3 x^{2}+8 x+5 a$
By factor theorem
If (x + 2) is the factor of f(x) then, f(-2) = 0
⟹ x + 2 = 0
⟹ x = -2
Substitute the value of x in f(x)
$f(-2)=4(-2)^{4}+2(-2)^{3}-3(-2)^{2}+8(-2)+5 a$
= 4(16) + 2(-8) - 3(4) - 16 + 5a
= 64 - 16 - 12 - 16 + 5a
= 5a + 20
equate f(-2) to zero
f(-2) = 0
⟹ 5a + 20 = 0
⟹ 5a = - 20
⟹ a = -20/5
⟹ a = - 4
When a = - 4, (x + 2) will be factor of f(x)
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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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