Find the value of k if x – 1 is a factor of p(x) in each of the following cases (i) p(x) = x2 + x + k (ii) p(x) = 2x2 + kx + √2 (iii) p(x) = kx2 – 2x + 1 (iv) p(x) = kx2 – 3x + k

Question 3. Find the value of k  if x – 1 is a factor of p(x) in each of the following cases:
(i) p(x) = x² + x + k
(ii) p(x) = 2x² + kx + √2
(iii) p(x) = kx² – 2x + 1
(iv) p(x) = kx² – 3x + k

(i) Find the value of k  if x – 1 is a factor of p(x) = x² + x + k
Apply remainder theorem
=>x - 1 =0
=> x =  1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get  
=> k(1)²  + 1+ 1 =0
=>k  +1 + 1 =0
=>  k  + 2 = 0
=> k = - 2 
Answer value of k = -2 

(ii) Find the value of k  if x – 1 is a factor of  p(x) = 2x² + kx + √2
Apply remainder theorem
=>x - 1 =0
=> x =  1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get  
p(1) = 2(1)² + k(1) + √2
p(1) =2 +  k  + √2
0 = 2 + √2 + k
-2 - √2 = k
- (2 + √2)  = k  
Answer is k = - (2 + √2) 

(iii) Find the value of k  if x – 1 is a factor of  p(x) = kx2 – √2x + 1
Apply remainder theorem
=>x - 1 =0
=> x =  1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get  
p(1) = k(1)² – √2(1)+ 1
P(1) = K - √2  + 1
0 = K - √2  + 1
√2  -1 = K
Answer k= √2 -1 


Find the value of k  if x – 1 is a factor of p(x)
(iv)Find the value of k  if x – 1 is a factor of  p(x) = kx² – 3x + k
Apply remainder theorem
=>x - 1 =0
=> x =  1
According to remainder theorem p(1) = 0 we get
Plug x = 1 we get 
P(1) = k(1)² -3(1) + k
0= k – 3 + k
0 = 2k – 3
3 = 2k
3/2 = k
Answer k = 3/2