If the expression (px3 + x2 – 2x – q) is divisible by (x – 1) an

1.	If the expression (px3 + x2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ?(a) 2, – 1 (b) –2, 1 (c) –2, –1 (d) 2, 1
Answer» (d) 2, 1 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.

If the expression (px3 + x2 – 2x – q) is divisible by (x – 1) and (x + 1), then the values of p and q respectively are ?(a) 2, – 1 (b) –2, 1 (c) –2, –1 (d) 2, 1

Answer»

(d) 2, 1

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.