Question

if x-1 is a factor of the polynomial p(x) = x³+ax²+2b and a+b=4 then​

Answer 1

Step-by-step explanation:

Since, x+1 is a factor of p(x)=2x

3

+ax

2

+2bx+1

Then, by factor theorem, p(−1)=0

⇒−2+a−2b+1=0⇒a−2b=1 ...(i)

Also,2a−3b=4 ...(ii)

On multiplying (i) by 2 and (ii) by 1, we get

2a−4b=2

−

2

a

+

−

3b=

−

4

−b=−2

∴b=2

On putting b=2 in (i), we get

a−2×2=1⇒a=5

∴a=5,b=2