Question

the polynomials ax3 +3x2 -13 and 2x3-5x+a leave the same remainder when divided by x+2,find a​

Answer 1

Step-by-step explanation:

Given polynomial p(x)=ax

3

+3x

2

−13 and 2x

2

−5x+a is divided by x-2 get same remainder

Then x-2=0 or x=2

p(x)=ax

3

+3x

2

−13

Replace x by 2 we get

p(2)=a(2)

3

+3(2)

2

−13

⇒p(2)=8a+12−13

⇒p(2)=8a−1

2x

2

−5x+a

Replace x by 2 we get

q(2)=2(2)

3

−5(2)+a

⇒q(2)=16−10+a

⇒q(2)=6+a

Given remainder is same

∴8a−1=6+a

⇒8a−1+1−a=6+a+1−a

⇒7a=7

a=1