Question

Solve the fllowing problem.

Answer 1

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If 2x³ +ax² + bx - 6 has (x - 1) as a factor and leaves a remainder 2 when divided by (x-2),find the relations between 'a' and 'b'

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→let f (x) = 2x³ + ax² + bx -6

→Since (x-1) is a factor of f (x),so by factor theorem ,we get

2.1³ + a.1 + b.1 -6 = 0

→ 2 + a + b - 6 = 0

→ a + b = 4

When f (x) is divided by (x - 2), it leaves a remainder 2.

So, 2.2³ + a.2² + b.2 - 6 =2

→ 16 + 4a +2b - 6= 2

→ 4a + 2b = 2-10

→ 4a + 2b = -8

→ 2a+b= -4

hence relation between a and b are a+b = 4 and 2a + b= -4