Question

find the value of 'a', if(x+a) is a factor of the polynomial x^3+ ax^2- 2x+a+4​

Answer 1

Answer:

a = 0.707 . please mark as brainlist

Step-by-step explanation:

given ,

x + a if a factor of x^3+ax^2-2x+a +4

p[-a]= [-a]^3+a[-a]^2-2[-a]+a+4=0

P[-a]= -a+a^2+2a+a+4=0

p[-a]=2a+a^2+4=0

p[-a]=2a+a^2=-4

p[-a]=a+a^2=-4/2

p[-a]= a+a = under root -2

p[-a] = a =1.414/2

therefore ,

a = 0.707

Answer 2

x+a is the factor of $x^3+ax^2-2x+a+4$

x+a = 0

x = -a

When we put value '-a' at the place of 'x'

we get,

$p(x)=x^3+ax^2-2x+a+4\\\\p(-a)=(-a)^3+a(-a)^2-2\times(-a)+a+4=0\\\\\implies-a^3+a^3+2a+a+4=0\\\\\implies2a+a+4=0\\\\\implies3a+4=0\\\\\implies3a=-4\\\\\implies\boxed{\bold{a=-\dfrac{3}{4}}}$

Therefore the value of 'a' is -3/4