Question

if X + 1 is a factor of 2 x cube + x square + 2 BHK + 1 then find the values of A and B given that 2A - 3 b - 4​

Answer 1

X+1 is a factor of 2x³+ax²+2bx+1

x+1 = 0

x = -1

→ 2(-1)³+a(-1)²+2b(-1)+1 = 0

→ 2(-1) + a(1) - 2b + 1 = 0

→ -2+a-2b+1 = 0

→ a-2b-1 = 0

→ a-2b = 1

Multiply it by 2,

2(a-2b) = 2(1)

2a-4b = 2 -----(1)

Given,

2a-3b = 0 ------(2)

(1) - (2)

2a-4b = 2

-{2a-3b = 0}

––––––––

-b = 2

b = -2

2a - 3(-2) = 0

2a+6 = 0

2a = -6

a = -6/2

a = -3

Therefore, a = -3 and b = -2

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