Question

find the value of a and b so that polynomial p of x is equal to x cube minus 3x cube minus ax plus b has (x+1) and (x-5) as factor​

Answer 1

Answer:

A = - 9, B = - 5

Step-by-step explanation:

Given : f(x) = x³ - 3x² + Ax + B

It is given that (x + 1) is a factor. So, it can make the whole polynomial equals to zero.

x + 1 = 0

x = - 1

f(- 1) = 0

→ (- 1)³ - 3(- 1)² + A(- 1) + B = 0

→ - 1 - 3 - A + B = 0

→ A - B = - 4 ...(i)

Also, (x - 5) is a factor.

x - 5 = 0

x = 5

f(5) = 0

→ (5)³ - 3(5)² + A(5) + B = 0

→ 125 - 75 + 5A + B = 0

→ 50 + 5A + B = 0

→ 5A + B = - 50 ...(ii)

Adding (i) and (ii), we get

6A = - 54

A = - 54/6

A = - 9

Put this value in (i), we get

- 9 - B = - 4

B = - 9 + 4

B = - 5