Question

if 2 X square + 3 X square + bx - 6 has X - 1 is a factor and leaves remainder 2 when divided by x minus 2 find the relation between a and b​

Answer 1

Answer:

Let the given polynomial be p(x) = x3 + ax2 + bx + 6

Given p(x) is divisible by (x – 2), hence p(2) = 0

Put x = 2 in p(x)

p(2) = 23 + a(2)2 + b(2) + 6

⇒ 0 = 8 + 4a + 2b + 6

⇒ 4a + 2b = – 14

⇒ 2a + b = – 7 → (1)

It is also given that when p(x) is divided by (x – 3) the remainder is 3

That p(3) = 3

Put x = 3 in p(x)

p(3) = 33 + a(3)2 + b(3) + 6

⇒ 3 = 27 + 9a + 3b + 6

⇒ 9a + 3b = – 30

⇒ 3a + b = – 10  → (2)

Subtract (2) from (1)

2a + b = – 7

3a + b = – 10 

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 – a = 3

∴ a = – 3

Substitute a = – 3 in (1), we get

2(– 3) + b = –7

∴ b = –1

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