Question

Find the values of a and b so that y^3 + 10y^2 + ay + b is exactly divisible by y - 1 and y - 2

Answer 1

Step-by-step explanation:

1. Calculate y with y-1=0 and y-2=0

y = 1 or 2

2. fill the values

(1) y^3 + 10y^2 + ay + b = 0

=> 0 = 1^3 + 10(1^2) + 1a + b

=> 0 = 1 + 10 + a + b

=> 0 = 11 + a + b

=> -11 = a + b

(2) y^3 + 10y^2 + ay + b= 0

=> 0 = 2^3 + 10(2^2) + 2a + b

=> 0 = 8 + 10(4) + 2a + b

=> 0 = 8 + 40 + 2a + b

=> 0 = 48 + 2a + b

=> -48 = 2a + b

3. calculate a and b

2a + b = -48

- a + b = -11

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a = -37

a + b = -11

=> -37 + b = -11

=> b = 37-11 = 26

Answer

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a=-37, b=26