Question

The value of p and q when px³ + x² - 2x - q is exactly divisible by (x - 1) and (x+1), is (a) 2,1 (b) 2,2 (c) 1, 1 (d) 1,0​

Answer 1

a

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Answer 2

Let f(x)=px

Let f(x)=px 3

Let f(x)=px 3 +x

Let f(x)=px 3 +x 2

Let f(x)=px 3 +x 2 −2x−q

Let f(x)=px 3 +x 2 −2x−qSince f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0.

Let f(x)=px 3 +x 2 −2x−qSince f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0.Therefore, p+1−2−q=0, i.e., p−q=1; and

Let f(x)=px 3 +x 2 −2x−qSince f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0.Therefore, p+1−2−q=0, i.e., p−q=1; and −p+1+2−q=0, i.e., p+q=3

Let f(x)=px 3 +x 2 −2x−qSince f(x) is divisible by (x−1) and (x+1) so x=1 and −1 must make f(x)=0.Therefore, p+1−2−q=0, i.e., p−q=1; and −p+1+2−q=0, i.e., p+q=3Thus p=2 and q=1