Question

find the values of A and B so that X + 1 and x minus 2 are the factors of x cube +a x square + 2X + b​

Answer 1

Answer

Step by step explanation

Answer 2

Answer:

Step-by-step explanation: Let f(x)= x³+ax²+2x+b and E₁=equation one

 x+1=0 and x-2=0

⇒x= -1 and x= 2

If (x+1) and (x-2) are factors of f(x), then f(-1)=0 and also f(2)=0

⇒ (-1³)+a(-1²)+2(-1)+b=0 and 2³+a(2²)+2(2)+b=0

⇒ -1+a-2+b=0 and 8+4a+4+b=0

⇒ a+b-3=0 and 4a+b+12=0

⇒ a+b= 3·······E₁ and 4a+b= -12········E₂

⇒  (a+b=3)

- (4a+b= -12)

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  -3a+0=15

⇒ -3a=15

⇒ a= -5········E₃

substitute E₃ in E₁

⇒ -5+b=3

⇒ b=3+5

⇒ b=8

∴ a= -5  and   b=8

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