Question

If (2x3 + ax2 + bx - 2) when divided by (2x-3) and (x+3) leaves reminders 7

and -2 Respectively, find the values of a and b.​

Answer 1

Answer:

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

x + 2) 2x3 + 3x2 - 3x - 2 (2x2 - x - 1 2x3 + 4x2 - .x² - 3x x2 - 2x + + -X - 2 -X + 2 x 2x2 - x - 1 2x2 - 2x + X - 1 2x (x - 1) +1 (x - 1) (x - 1) (2x + 1) Hence required factors are (x - 1) (x + 2) (2x + 1)

Answer 2

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here's your answer

┗━━━━•❅•°•❈ ↯ •°•❅•━━━━┛

Lymphocytes ✍

✒They have round shaped nucleus.

Monocytes ✍

✒They have horseshoe shaped or kidney shaped nucleus.

✥Hope it helps❢❢

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