Question

If
x-2 is the factor of x^3 +ax^2+bx+16 and
a-b=6. Find the val ue of and b​

Answer 1

Answer:

a = - 2, b = - 8

Step-by-step explanation:

Given : f(x) = x³ + ax² + bx + 16

It is given that (x - 2) is a factor of above polynomial. So, it will make the whole polynomial equals to zero.

x - 2 = 0

x = 2

f(2) = 0

→ (2)³ + a(2)² + b(2) + 16 = 0

→ 8 + 4a + 2b + 16 = 0

→ 4a + 2b + 24 = 0

→ 2a + b + 12 = 0

→ 2a + b = - 12 ...(i)

a - b = 6 ...(ii) [given]

Adding (i) and (ii), we get

3a = - 6

a = - 6/3

a = - 2

Put this value in (ii), we get

- 2 - b = 6

b = - 2 - 6

b = - 8