Question

find the values of a and b so that (2x^3 + ax^2 + x + b) has (x + 2) and (2x - 1) as factors.​

Answer 1

p(x)=2x^3+ax^2+x+b

g(x)=x+2

g(x)=0

x+2=0

x=-2

p(-2)=2*(-2)^3+a*(-2)^2+(-2)+b

=2*(-8)+a*4-2+b

=-16+4a-2+b

=-18+4a+b

=4a+b=18

=a=(18-b)/4

g(x)=2x-1

g(x)=0

2x-1=0

2x=1

x=1/2

p(1/2)=2*(1/2)^3+[(18-b)/4](1/2)^2+1/2+b=0

=2*1/8+[(18-b)/4]*1/4+1/2+b=0

=1/4+(18-b)/16+1/2+b=0

=(4+18-b+8+16b)/16=0

(40+15b)/16=0

40+15b=0

15b=-40

b=-40/15

b=-8/3

a=[18-(-8/3)]/4

a=[18+8/3]/4

a=[(54+8)/3]/4

a=[62/3]/4

a=(62*4)/3

a=66/3

a=22

a=22 and b=-8/3 ans