Question:
If $x=-1 / 2$ is zero of the polynomial $p(x)=8 x^{3}-a x^{2}-x+2$, Find the value of a
Solution:
We know that, $p(x)=8 x^{3}-a x^{2}-x+2$
Given that the value of x = -1/2
Substitute the value of x in f(x)
$p(-1 / 2)=8(-1 / 2)^{3}-a(-1 / 2)^{2}-(-1 / 2)+2$
= - 8(1/8) - a(1/4) + 1/2 + 2
= -1 - (a/4 + 1/2 + 2)
= 1 - (a/4 + 1/2)
= 3/2 − a/4
To, find the value of a, equate p(-1/2) to zero
p(-1/2) = 0
3/2 - a/4 = 0
On taking L.C.M
$\frac{6-a}{4}=0$
$\Rightarrow 6-a=0$
$\Rightarrow a=6$
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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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