Question

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The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.


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Answer 1

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Answer 2

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☆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

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