Question

if the polynomial x^3+ax^2+5 and x^3-2x^2+a are divided by (x+2) leave the same remainder ,find the value of a​

Answer 1

Answer:

Given polynomial x

3

+ax

2

+5 and x

3

−2x

2

+a divided by x+2 the remainder is same

Then x+2=0 or x=−2 replace x by −2 we get

p(x)=x

3

+ax

2

+5

p(−2)=(−2)

3

+a(−2)

2

+5

⇒p(2)=−8+a×4+5

⇒P(2)=4a−8+5

⇒p(2)=4a−3

q(x)=x

3

−2x

2

+a

⇒q(−2)=(−2)

3

−2(−2)

2

+a

⇒q(2)=−8−8+a

⇒A(2)=a−16

∴4a−3=a−16

Subtract a and add 3 both the sides we get,

4a−3−a+3=a−16−a+3

⇒3a=−13

Divided both side by 3 we get

a=−

3

13