Question

If (x + 1) is a factor of 2x3 + ax2 + 2bx + 1, then find the values of a and b given that 2a 3b = (a) a = 1, b = 2 (b) a = 2, b = 5 (c) a = 5, b = 2 (d) a = 2, b = 0

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

Answer 2

Step-by-step explanation:

2(-1)+a(1)+2b(-1)+1 =0

-2+a-2b+1=0

-1+a-2b=0