Question

on dividing x3 + ax2 + 19x + 20 by ( x+3 ), if the remainder is a, then find the value of a.​

Answer 1

Answer:

a=8

Step-by-step explanation:

Let f(x)=x^3+ax^2+19x+20

divisor=x+3

by factors theorem x+3=0=>x=-3

given f(-3)=a

=>(-3)^3+a(-3)^2+19(-3)+20=a

=>-27+a(9)-57+20=a

=>9a-64=a

=>9a-a=64

=>8a=64

=>a=64/8

=>a=8

Answer 2

The value of a is 8.

Given:

On dividing (x³ + ax² + 19x + 2) by ( x+3 ), the remainder is a.

To Find:

We have to find the value of a.

Solution:

This is a simple problem for division.

Let us tackle this problem.

We can easily solve this problem  as follows,

Let,

f(x)=x³+ax²+19x+20

Divisor=x+3

By factors theorem,

x+3=0

⇒x= -3

Given f(-3)=a

⇒ (-3)³+a(-3)²+19(-3)+20 = a

⇒ -27+a(9)-57+20 = a

⇒ 9a-64 = a

⇒ 9a-a = 64

⇒ 8a = 64

⇒ a = 64÷8

⇒ a = 8

Hence, the value of a is 8.

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