"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) = x^2 + x + k
(ii) p(x) = 2x^2 + kx + 2^(1/2)
(iii) p(x) = kx^2 - 2^(1/2) x + 1
(iv) p(x) = kx^2 − 3x + k
Class 9 - Math - Polynomials Page 44"
Answers
Solution;
i) If x – 1 is a factor of polynomial p(x) = x²+ x + k, then
p(1) = 0
On putting X= 1
⇒ (1)² + 1 + k =
0
⇒ 2
+ k = 0
⇒ k = – 2
Hence, the value of k is -2.
(ii) If x – 1 is a
factor of polynomial p(x) = 2x² + kx + √2, then
p(1) = 0
On putting x= 1
⇒ 2(1)² + k(1)
+ √2 = 0
⇒ 2
+ k + √2 =
0
⇒ k = -2 – √2
K= -(2 + √2)
Therefore, value of k is -(2 + √2).
(iii) If x – 1 is a
factor of polynomial p(x) = kx² – √2x + 1, then
p(1) = 0
On putting x= 1
⇒ k(1)²– √2(1) +
1 = 0
⇒ k – √2 + 1 = 0
⇒ k = √2 – 1
Hence, the value of k is √2 – 1.
(iv) If x – 1 is a
factor of polynomial p(x) = kx² – 3x + k, then
p(1) = 0
On putting x= 1
⇒ k(1)² + 3(1)
+ k = 0
⇒ k – 3 + k = 0
⇒ 2k – 3 = 0
⇒ k = 3/2
Hence, the value of k = 3/2.
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