Question

if 2x^3+px^2 +q x-2 has a factor [x+2] and leaves remainder7 when divided by [2x-3] find the value of p and q

Answer 1

Step-by-step explanation:

Let P(x) = 2x3 + ax2 + bx – 2

when P(x) is divided by 2x – 3

P(3/2) = 2(3/2)3 + a(3/2)2 + b(3/2) – 2 = 7

= 27/4 + 9/4a + 3/2b – 2 = 7

= 27 + 9a + 6b – 8/4 = 7

= 9a + 6b = 28 + 8 – 27

= 9a + 6b = 9

⇒ 3a + 2b = 3 ….(1)

Similarly when P(x) is divided by x + 2

x = - 2

2(- 2)3 + a(- 2)2 + b(- 2) – 2 = 0

-16 + 4a – 2b – 2 = 0

⇒ 4a – 2b = 18 ….(2)

On solving equation (1) and (2)

On substituting value of a in equation (1)

3 3 + 2b = 3

2b = 3 – 9

b = -6/2 = - 3

b = - 3

a = 3, b = - 3

On substituting value of a and b

2x3 + 3a2 – 3x – 2

When x + 2 is factor