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

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here is ur answer

Answer 2

a = 5 and b = 2

Given is the value of a and b.

given that (x+1) is a factor of p(x)

therefore, -1 is a zero of given p(x)

p(x) = 2x3 +ax2 +2bx +1

substituting the value of -1 in the given p(x),we get

p(x)=2*(-1)3 +a *(-1)2 +2*b*(-1)+ 1

 = -2 + a -2b + 1

= -1 + a - 2b

or,a - 2b = 1

also given that 2a - 3b = 4

so we got two equations;

a - 2b = 7 ...(1)

2a - 3b = 4 ...(2)

(1)* (2)* (4)- 2 = 2a - 4b = (3)

(2)* 1 = 2a - 3b = 4 (4)

(4) -  (3) = [2a - 2a ] + [-3b - (-4b)] = 4 - 2

-3b + 4b = 2

therefore b = 2

substituting the value of b in (3)

2a - 4b = 2

2a - (4*2) = 2

2a - 8 = 2

2a = 2 + 8

2 = 10

a = 10 / 2

therefore a = 5

so we get the value of a and b

that is ; a = 5 and b = 2