Question

If (x - 2) is a factor of (x - 1)^5 – (2x + 3k)^2, then the value of k is? ​

Answer 1

Answer:

k=-1

Step-by-step explanation:

x=2

(2-1)power5-(2x2+3xk)power2=0

1power5-(4+3k)power2=0

1=(4+3k)power2  (a+b)2=a2+2ab+b2

1=16+9kpower2+24k

1=16+9(-1)power2+24(-1)

Equating k=-1

Answer 2

Answer:

If (x -2) is a factor of polynomial p(x) then,

p(x) =0 for x =2,

as given p(x)= (x-1)^5 -(2x +3k)^2 = 0

(2 -1)^5 - (2*2+ 3k)^2=0

(1)^5- (4 -3k)^2 =0

1 - 16 -24k + 9k^2 =0

9k^2 - 24k -15 =0

3(3k^2 - 8k -5) =0

3k^2 -8k -5 =0

3k(k - 1)- 5(k-1) =0

(k-1)(3k -5)=0

k=1 or k= 5/3 ans.