Question

If x + 1 is a factor of x⁴ + (p - 3) x³ - (3p-5)x² +(2p - 9) x + 6 ,
then the value of p is
(a) - 4 (b) 0 (c) 4 (d) 2

Answer 1

Answer:

4

c). option is correct.

Step-by-step explanation:

Given :

p ( x ) = x⁴ + ( p - 3 ) x³ - ( 3 p - 5 ) x² +( 2 p - 9 ) x + 6

Also x + 1 is a factor of p ( x )

Since it is factor it will satisfy the value for equation :

= > x + 1 = 0

= > x = - 1

Now :

p ( - 1 ) = ( - 1 )⁴ + ( p - 3 ) ( - 1 )³ - (3 p - 5 ) ( - 1 )² +( 2 p - 9 ) ( - 1 ) + 6

p ( - 1 ) = 1 - ( p - 3 ) - (3 p - 5 ) - ( 2 p - 9 ) + 6

Equating with zero :

1 - ( p - 3 ) - (3 p - 5 ) - ( 2 p - 9 ) + 6 = 0

= > - p + 3 - 3 p + 5 - 2 p + 9 + 7 = 0

= > - 6 p + 24 = 0

= > 6 p = 24

= > 6 p = 6 ( 4 )

= > p = 4

Hence the value of p is 4 .