ANSWER THIS AND GET 25 POINTS. ——————————————————————————-|. Find the value of (K)' if x-1 is a factor of p(x) in each of following a) p(x)=x^2+x+k. b) p(x)=2x^2+Kx + route 2 c)p(x)=kx^2-route2x+1.
d) p(x)=kx^2-3x+k
Answers
Answer:
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
Solution: (i) 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) 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) 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
(iv) 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