Question

if the polynomial x cube +a x square + 5 and x cube minus 2 X square + a divided by X + two leave the same remainder find the value of a ​

Answer 1

Answer:

The value of a is -13/3

Step-by-step explanation:

Concept used:

$\boxed{\text{Remainder theorem: The remainer when P(x) is divided by (x+a) is P(-a)}}$

$\text{Let p(x)=x^3+ax^2+5 and q(x)=x^3-2x^2+a }$

Given: when p(x) and q(x) is divided by (x+2), $p(-2)=q(-2)$

$\implies\:(-2)^3+a(-2)^2+5=(-2)^3-2(-2)^2+a$

$\implies\:-8+4a+5=-8-8+a$

$\implies\:4a-3=a-16$

$\implies\:4a-a=3-16$

$\implies\:3a=-13$

$\implies\:\boxed{a=\frac{-13}{3}}$

Answer 2

The value of a is -13/3

Step-by-step explanation:

Concept used:

\boxed{\text{Remainder theorem: The remainer when P(x) is divided by (x+a) is P(-a)}}

Remainder theorem: The remainer when P(x) is divided by (x+a) is P(-a)

\text{Let $p(x)=x^3+ax^2+5$ and $q(x)=x^3-2x^2+a$}Let p(x)=x

3

+ax

2

+5 and q(x)=x

3

−2x

2

+a

Given: when p(x) and q(x) is divided by (x+2), p(-2)=q(-2)p(−2)=q(−2)

\implies\:(-2)^3+a(-2)^2+5=(-2)^3-2(-2)^2+a⟹(−2)

3

+a(−2)

2

+5=(−2)

3

−2(−2)

2

+a

\implies\:-8+4a+5=-8-8+a⟹−8+4a+5=−8−8+a

\implies\:4a-3=a-16⟹4a−3=a−16

\implies\:4a-a=3-16⟹4a−a=3−16

\implies\:3a=-13⟹3a=−13

\implies\:\boxed{a=\frac{-13}{3}}⟹

a=

3

−13