Question

The value of p and q when px^3 + x^2 - 2x - q is exactly divisible by (x-1) and (x+1), is


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Answer 1

Answer:

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=1

Step-by-step explanation:

Let f(x)=px

3

+x

2

−2x−q

Since 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

Thus p=2 and q=1

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Answer 2

Answer:

px3 + x2 – 2x – q is divisible by (x – 1) and (x + 1) ⇒ p(1)3 + (1)2 – 2(1) – q = 0 ⇒ p – q = 1 ...(i) and p(–1)3 + (–1)2 – 2(–1) – q = 0 ⇒ p + q = 3 ...(ii) Solving (i) and (ii) p = 2, q = 1.Read more on Sarthaks.com - https://www.sarthaks.com/1000672/if-the-expression-px-x-2-2x-q-is-divisible-by-x-and-x-1-then-the-values-of-p-and-respectively-are