Question

8. If x3 - px2 + qx + 6 has (x – 1) as a factor an
leaves a remainder 4 when divided by (x + 1),
find the values of p and q.
​

Answer 1

Answer:

p = 11 and q = 4

Step-by-step explanation:

When f(x) is divided by (x + 1) and (x - 1), the remainders are 4 and 0 respectively.

Therefore, f(x) = x3 - px2 + qx +6

x + 1 = 0

x = - 1

f(- 1) = (- 1)3 - p(- 1)2 + q(-1) + 6

=> - 1 - 1p + q - 1 + 6

=> - 1 + 6 - 1p + q - 1

=> 5 - 1 - 1p + q = 0

=> 4 - 1p + q = 0

=> - 1p + q = - 4 (i)

f(x) = x3 - px2 + qx + 6

x - 1 = 0

x = 1

=> (1)3 - p(1)2 + q(1) + 6

=> 1 - 1p + 1q + 6

=> - 1p + 1q + 6 + 1 = 0

=> - 1p + 1q + 7 = 0

=> - 1p + 1q = - 7 (ii)

On subtracting (i) and (ii), we get

- 1p + q - (- 1p + 1q) = - 4 - (- 7)

p = - 4 + 7

= 3

On putting P in (ii), we get

1(3) + q = - 7

q = - 7 + 3

= - 4

so, the answer of value of P and Q will be 3 and - 4.