Question

Find the value of a ,b so that (2x^3+ax^2+x+b) has (x+2)&(x-1)as a factor

Answer 1

here is ur answer....

Answer 2

Let x+2 = 0
x = -2
${2x}^{3} + {ax}^{2} + 2x + b \\ 2( - 2)^{3} + a( - 2)^{2} + 2( - 2) + b = 0 \\ - 16 + 4a - 4 + b = 0 \\ - 20 + 4a + b = 0 \\ 4a + b = 20 \: \: \: \: \: \: \: .......(i) \:$
Let x-1 = 0
x = 1
$2{(1)}^{3} + a {(1)}^{2} + 2(1) + b = 0 \\ 2 + a + 2 + b = 0 \\ 4 + a + b = 0 \\ a + b = - 4 \: \: \: \: \: \: \: ..........(ii)$
Subtracting (ii) from (i)
4a + b = 20
a + b = - 4
- - +
3a = 24
a = 24/3
a = 8
Putting value of a in (ii)
8 + b = - 4
b = - 4 - 8
b = - 12

a = 8 ; b = - 12