Question

If (x+1) is a factor of 2x^3+ax^2+2bx+1,then find the values of a and b given that 2a-3b=4​

Answer 1

Answer:

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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Answer 2

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