Question

find the value of A and B so that x-1 and X + 2 are factors of f(x)=2x^3+ax^2+bx-14​

Answer 1

Answer:

As x-1is a factor of f(x)

x-1=0

x=1

f(1)=2×1^3+a×1^2+b×1-14

0 =2+a+b-14

= -12+a+b__________(i)

As x+2 is a factor of f(x)

x+2=0

x=-2

f(-2)=2×(-2)^3+ a(-2)^2+b(-2)-14

0 =2×-8 +4a -2b -14

=-16+4a+2b-14

= -30 +4a +2b_________(ii)

from ( i) and (ii)

-12+a+b= -30+4a+2b

-12+30=4a+2b-a-b

18=3a+b

3a=1

a=1/3

b=18