Question

Find the value of a and b if x+2 is a factor or f(x) = ax^3 - bx^2 + 2(x-2) and f(2) = 20


ans : a = 3/2 b = -7/2​

Answer 1

Answer:

As x

2

+x−2=(x+2)(x−1)

Let f(x)=ax

4

+bx

3

−x

2

+2x+3=(x

2

+x−2)Q(x)+4x+3, where Q(x) is the quotient

Then,

f(−2)=a(−2)

4

+b(−2)

3

−(−2)

2

+2(−2)+3=4(−2)+3

⇒16a−8b−4−4+3=−5⇒2a−b=0 ......... (1)

And

f(1)=a+b−1+2+3=4(1)+3⇒a+b=3 ........ (2)

Solving (1) and (2) simultaneously, we get

a=1,b=2