Question

The polynomials bx^3+3x^2-3 and 2x^3-5x+b leave the remainder R1 and R2 respectively. If 2R1-R1 = 0 then find the value of b.

Answer 1

Let the remainder be R1 and R2 as given :

R1 = bx^3 + 3x^2 - 3

Now, x - 4 => x = 4

R1 = b(4)^3 + 3(4)^2 - 3

R1 = 64b + 48 - 3

R1 = 64b + 45

R2 = 2x^2 - 5x + b

R2 = 2(4)^2 - 5(4) + b

R2 = 32 - 20 + b

R2 = 12 + b

R1 + R2 = 0

64b + 45 + 12 + b = 0

65b = - 57

B = - 57/65

2R1 - R2 = 0

2( 64b + 45 ) - 12 - b = 0

128b + 90 - 12 - b = 0

127b = - 78

b = - 78/127

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